ScaDaMaLe Course site and book

This notebook is from databricks document: - https://docs.databricks.com/_static/notebooks/package-cells.html

As you know, we need to eventually package and deploy our models, say using sbt.

However it is nice to be in a notebook environment to prototype and build intuition and create better pipelines.

Using package cells we can be in the best of both worlds to an extent.

Package Cells

Package cells are special cells that get compiled when executed. These cells have no visibility with respect to the rest of the notebook. You may think of them as separate scala files.

This means that only class and object definitions may go inside this cell. You may not have any variable or function definitions lying around by itself. The following cell will not work.

If you wish to use custom classes and/or objects defined within notebooks reliably in Spark, and across notebook sessions, you must use package cells to define those classes.

Unless you use package cells to define classes, you may also come across obscure bugs as follows:

// We define a class
case class TestKey(id: Long, str: String)
defined class TestKey
// we use that class as a key in the group by
val rdd = sc.parallelize(Array((TestKey(1L, "abd"), "dss"), (TestKey(2L, "ggs"), "dse"), (TestKey(1L, "abd"), "qrf")))

rdd.groupByKey().collect
rdd: org.apache.spark.rdd.RDD[(TestKey, String)] = ParallelCollectionRDD[0] at parallelize at command-2971213210276613:2
res0: Array[(TestKey, Iterable[String])] = Array((TestKey(1,abd),CompactBuffer(dss)), (TestKey(1,abd),CompactBuffer(qrf)), (TestKey(2,ggs),CompactBuffer(dse)))

What went wrong above? Even though we have two elements for the key TestKey(1L, "abd"), they behaved as two different keys resulting in:

Array[(TestKey, Iterable[String])] = Array(
  (TestKey(2,ggs),CompactBuffer(dse)), 
  (TestKey(1,abd),CompactBuffer(dss)), 
  (TestKey(1,abd),CompactBuffer(qrf)))

Once we define our case class within a package cell, we will not face this issue.

package com.databricks.example

case class TestKey(id: Long, str: String)
Warning: classes defined within packages cannot be redefined without a cluster restart.
Compilation successful.
import com.databricks.example

val rdd = sc.parallelize(Array(
  (example.TestKey(1L, "abd"), "dss"), (example.TestKey(2L, "ggs"), "dse"), (example.TestKey(1L, "abd"), "qrf")))

rdd.groupByKey().collect
import com.databricks.example
rdd: org.apache.spark.rdd.RDD[(com.databricks.example.TestKey, String)] = ParallelCollectionRDD[2] at parallelize at command-2971213210276616:3
res2: Array[(com.databricks.example.TestKey, Iterable[String])] = Array((TestKey(1,abd),CompactBuffer(dss, qrf)), (TestKey(2,ggs),CompactBuffer(dse)))

As you can see above, the group by worked above, grouping two elements (dss, qrf) under TestKey(1,abd).

These cells behave as individual source files, therefore only classes and objects can be defined inside these cells.

package x.y.z

val aNumber = 5 // won't work

def functionThatWillNotWork(a: Int): Int = a + 1

The following cell is the way to go.

package x.y.z

object Utils {
  val aNumber = 5 // works!
  def functionThatWillWork(a: Int): Int = a + 1
}
Warning: classes defined within packages cannot be redefined without a cluster restart.
Compilation successful.
import x.y.z.Utils

Utils.functionThatWillWork(Utils.aNumber)
import x.y.z.Utils
res5: Int = 6

Why did we get the warning: classes defined within packages cannot be redefined without a cluster restart?

Classes that get compiled with the package cells get dynamically injected into Spark's classloader. Currently it's not possible to remove classes from Spark's classloader. Any classes that you define and compile will have precedence in the classloader, therefore once you recompile, it will not be visible to your application.

Well that kind of beats the purpose of iterative notebook development if I have to restart the cluster, right? In that case, you may just rename the package to x.y.z2 during development/fast iteration and fix it once everything works.

One thing to remember with package cells is that it has no visiblity regarding the notebook environment.

  • The SparkContext will not be defined as sc.
  • The SQLContext will not be defined as sqlContext.
  • Did you import a package in a separate cell? Those imports will not be available in the package cell and have to be remade.
  • Variables imported through %run cells will not be available.

It is really a standalone file that just looks like a cell in a notebook. This means that any function that uses anything that was defined in a separate cell, needs to take that variable as a parameter or the class needs to take it inside the constructor.

package x.y.zpackage

import org.apache.spark.SparkContext

case class IntArray(values: Array[Int])

class MyClass(sc: SparkContext) {
  def sparkSum(array: IntArray): Int = {
    sc.parallelize(array.values).reduce(_ + _)
  }
}

object MyClass {
  def sparkSum(sc: SparkContext, array: IntArray): Int = {
    sc.parallelize(array.values).reduce(_ + _)
  }
}
Warning: classes defined within packages cannot be redefined without a cluster restart.
Compilation successful.
import x.y.zpackage._

val array = IntArray(Array(1, 2, 3, 4, 5))

val myClass = new MyClass(sc)
myClass.sparkSum(array)
import x.y.zpackage._
array: x.y.zpackage.IntArray = IntArray([I@44a91426)
myClass: x.y.zpackage.MyClass = x.y.zpackage.MyClass@5d3b142
res7: Int = 15
MyClass.sparkSum(sc, array)
res8: Int = 15

Build Packages Locally

Although package cells are quite handy for quick prototyping in notebook environemnts, it is better to develop packages locally on your laptop and then upload the packaged or assembled jar file into databricks to use the classes and methods developed in the package.

ScaDaMaLe Course site and book

Core ideas in Monte Carlo simulation

  • modular arithmetic gives pseudo-random streams that are indistiguishable from 'true' Uniformly distributed samples in integers from \({0,1,2,...,m}\)
  • by diving the integer streams from above by \(m\) we get samples from \({0/m,1/m,...,(m-1)/m}\) and "pretend" this to be samples from the Uniform(0,1) RV
  • we can use inverse distribution function of von Neumann's rejection sampler to convert samples from Uniform(0,1) RV to the following:
    • any other random variable
    • vector of random variables that could be dependent
    • or more generally other random structures:
      • random graphs and networks
      • random walks or (sensible perturbations of live traffic data on open street maps for hypothesis tests)
      • models of interacting paticle systems in ecology / chemcal physics, etc...

breeze.stats.distributions

Breeze also provides a fairly large number of probability distributions. These come with access to probability density function for either discrete or continuous distributions. Many distributions also have methods for giving the mean and the variance.

import breeze.stats.distributions._

val poi = new Poisson(3.0);
import breeze.stats.distributions._
poi: breeze.stats.distributions.Poisson = Poisson(3.0)
val s = poi.sample(5); // let's draw five samples - black-box
s: IndexedSeq[Int] = Vector(2, 4, 3, 4, 6)

Getting probabilities of the Poisson samples

s.map( x => poi.probabilityOf(x) ) // PMF
res0: IndexedSeq[Double] = Vector(0.22404180765538775, 0.16803135574154085, 0.22404180765538775, 0.16803135574154085, 0.05040940672246224)
val doublePoi = for(x <- poi) yield x.toDouble // meanAndVariance requires doubles, but Poisson samples over Ints
doublePoi: breeze.stats.distributions.Rand[Double] = MappedRand(Poisson(3.0),$Lambda$5909/1062631843@70cdbd4c)
breeze.stats.meanAndVariance(doublePoi.samples.take(1000));
res1: breeze.stats.meanAndVariance.MeanAndVariance = MeanAndVariance(3.0660000000000034,3.250894894894892,1000)
(poi.mean, poi.variance) // population mean and variance
res2: (Double, Double) = (3.0,3.0)

Exponential random Variable

Let's focus on getting our hands direty with a common random variable.

NOTE: Below, there is a possibility of confusion for the term rate in the family of exponential distributions. Breeze parameterizes the distribution with the mean, but refers to it as the rate.

val expo = new Exponential(0.5);
expo: breeze.stats.distributions.Exponential = Exponential(0.5)
expo.rate // what is the rate parameter
res3: Double = 0.5

A characteristic of exponential distributions is its half-life, but we can compute the probability a value falls between any two numbers.

expo.probability(0, math.log(2) * expo.rate)
res4: Double = 0.5
expo.probability(math.log(2) * expo.rate, 10000.0)
res5: Double = 0.5
expo.probability(0.0, 1.5)
res6: Double = 0.950212931632136

The above result means that approximately 95% of the draws from an exponential distribution fall between 0 and thrice the mean. We could have easily computed this with the cumulative distribution as well.

1 - math.exp(-3.0) // the CDF of the Exponential RV with rate parameter 3
res7: Double = 0.950212931632136
val samples = expo.sample(2).sorted; // built-in black box - we will roll our own shortly in Spark
samples: IndexedSeq[Double] = Vector(2.412493444974671, 3.6802759985818687)
expo.probability(samples(0), samples(1));
res8: Double = 0.007390811722912227
breeze.stats.meanAndVariance(expo.samples.take(10000)); // mean and variance of the sample
res9: breeze.stats.meanAndVariance.MeanAndVariance = MeanAndVariance(2.0109026469746554,4.073504140726905,10000)
(1 / expo.rate, 1 / (expo.rate * expo.rate)) // mean and variance of the population
res10: (Double, Double) = (2.0,4.0)
import spark.implicits._
import org.apache.spark.sql.functions._
import spark.implicits._
import org.apache.spark.sql.functions._
val df = spark.range(1000).toDF("Id") // just make a DF of 1000 row indices
df: org.apache.spark.sql.DataFrame = [Id: bigint]
df.show(5)
+---+
| Id|
+---+
|  0|
|  1|
|  2|
|  3|
|  4|
+---+
only showing top 5 rows
val dfRand = df.select($"Id", rand(seed=1234567) as "rand") // add a column of random numbers in (0,1)
dfRand: org.apache.spark.sql.DataFrame = [Id: bigint, rand: double]
dfRand.show(5) // these are first 5 of the 1000 samples from the Uniform(0,1) RV
+---+--------------------+
| Id|                rand|
+---+--------------------+
|  0|0.024042816995877625|
|  1|  0.4763832311243641|
|  2|  0.3392911406256911|
|  3|  0.6282132043405342|
|  4|  0.9665960987271114|
+---+--------------------+
only showing top 5 rows
val dfRand = df.select($"Id", rand(seed=1234567) as "rand") // add a column of random numbers in (0,1)
dfRand.show(5) // these are first 5 of the 1000 samples from the Uniform(0,1) RV
+---+--------------------+
| Id|                rand|
+---+--------------------+
|  0|0.024042816995877625|
|  1|  0.4763832311243641|
|  2|  0.3392911406256911|
|  3|  0.6282132043405342|
|  4|  0.9665960987271114|
+---+--------------------+
only showing top 5 rows

dfRand: org.apache.spark.sql.DataFrame = [Id: bigint, rand: double]
val dfRand = df.select($"Id", rand(seed=879664) as "rand") // add a column of random numbers in (0,1)
dfRand.show(5) // these are first 5 of the 1000 samples from the Uniform(0,1) RV
+---+-------------------+
| Id|               rand|
+---+-------------------+
|  0|  0.269224348263137|
|  1|0.20433965628039852|
|  2| 0.8481228617934538|
|  3| 0.6665103087537884|
|  4| 0.7712898780552342|
+---+-------------------+
only showing top 5 rows

dfRand: org.apache.spark.sql.DataFrame = [Id: bigint, rand: double]

Let's use the inverse CDF of the Exponential RV to transform these samples from the Uniform(0,1) RV into those from the Exponential RV.

val dfRand = df.select($"Id", rand(seed=1234567) as "rand") // add a column of random numbers in (0,1)
               .withColumn("one",lit(1.0))
               .withColumn("rate",lit(0.5))
dfRand: org.apache.spark.sql.DataFrame = [Id: bigint, rand: double ... 2 more fields]
dfRand.show(5) 
+---+--------------------+---+----+
| Id|                rand|one|rate|
+---+--------------------+---+----+
|  0|0.024042816995877625|1.0| 0.5|
|  1|  0.4763832311243641|1.0| 0.5|
|  2|  0.3392911406256911|1.0| 0.5|
|  3|  0.6282132043405342|1.0| 0.5|
|  4|  0.9665960987271114|1.0| 0.5|
+---+--------------------+---+----+
only showing top 5 rows
val dfExpRand = dfRand.withColumn("expo_sample", -($"one" / $"rate") * log($"one" - $"rand")) // samples from expo(rate=0.5)
dfExpRand: org.apache.spark.sql.DataFrame = [Id: bigint, rand: double ... 3 more fields]
dfExpRand.show(5)
+---+--------------------+---+----+--------------------+
| Id|                rand|one|rate|         expo_sample|
+---+--------------------+---+----+--------------------+
|  0|0.024042816995877625|1.0| 0.5|0.048673126808362034|
|  1|  0.4763832311243641|1.0| 0.5|  1.2939904386814756|
|  2|  0.3392911406256911|1.0| 0.5|  0.8288839819270684|
|  3|  0.6282132043405342|1.0| 0.5|  1.9788694379168241|
|  4|  0.9665960987271114|1.0| 0.5|   6.798165162486205|
+---+--------------------+---+----+--------------------+
only showing top 5 rows
display(dfExpRand)
Id rand one rate expo_sample
0.0 2.4042816995877625e-2 1.0 0.5 4.8673126808362034e-2
1.0 0.4763832311243641 1.0 0.5 1.2939904386814756
2.0 0.3392911406256911 1.0 0.5 0.8288839819270684
3.0 0.6282132043405342 1.0 0.5 1.9788694379168241
4.0 0.9665960987271114 1.0 0.5 6.798165162486205
5.0 0.8269758822163711 1.0 0.5 3.508648570093974
6.0 0.3404052214826948 1.0 0.5 0.8322592089262
7.0 0.5658253891225227 1.0 0.5 1.6686169931673005
8.0 0.11737981749647353 1.0 0.5 0.24972063061386013
9.0 0.7848668745585088 1.0 0.5 3.072996508744745
10.0 0.10665116151243736 1.0 0.5 0.2255562755600773
11.0 0.34971775733163646 1.0 0.5 0.8606975816973311
12.0 3.349566781262969e-2 1.0 0.5 6.813899599567436e-2
13.0 0.334063669089834 1.0 0.5 0.8131224244912618
14.0 0.4105052702588069 1.0 0.5 1.0569789985263547
15.0 0.22519777483698333 1.0 0.5 0.5102949510683874
16.0 0.21124107883891907 1.0 0.5 0.47458910937069004
17.0 0.12332274767843698 1.0 0.5 0.26323273531964136
18.0 4.324422155449681e-2 1.0 0.5 8.841423006745963e-2
19.0 3.933267172708754e-2 1.0 0.5 8.025420479220831e-2
20.0 0.8162723223794007 1.0 0.5 3.388601261211285
21.0 7.785566240785313e-2 1.0 0.5 0.16210703862675058
22.0 0.1244015150504949 1.0 0.5 0.26569528726942954
23.0 0.5313795676534989 1.0 0.5 1.5159243018004147
24.0 0.8177063965639969 1.0 0.5 3.4042733720631824
25.0 0.7757379079578416 1.0 0.5 2.98987971469377
26.0 0.9019086568714294 1.0 0.5 4.643712323362237
27.0 0.5793202308042869 1.0 0.5 1.7317667559523853
28.0 4.913530139386124e-2 1.0 0.5 0.10076699863506142
29.0 0.6984668419742928 1.0 0.5 2.3977505839877837
30.0 1.579141234703818e-2 1.0 0.5 3.18348501444197e-2
31.0 0.3170147319677016 1.0 0.5 0.762563978285606
32.0 0.6243818511105477 1.0 0.5 1.9583644261768265
33.0 0.9720896733059052 1.0 0.5 7.157517052464175
34.0 6.406755887221727e-2 1.0 0.5 0.13242396678361196
35.0 0.8275324400058236 1.0 0.5 3.515092236401242
36.0 0.4223760255739688 1.0 0.5 1.0976643705892708
37.0 0.6237792697270514 1.0 0.5 1.9551585184791915
38.0 0.30676209726152626 1.0 0.5 0.7327640894184466
39.0 0.7209798363387625 1.0 0.5 2.5529424571699533
40.0 0.5408086036735253 1.0 0.5 1.556576340750279
41.0 0.22254408000797787 1.0 0.5 0.5034566621599345
42.0 0.6478051949133747 1.0 0.5 2.0871416658496442
43.0 0.6186563924196967 1.0 0.5 1.9281089062362353
44.0 0.2689179760895458 1.0 0.5 0.6264592354306907
45.0 0.1310898372764776 1.0 0.5 0.28103107825164747
46.0 0.8459785027719904 1.0 0.5 3.741326187841892
47.0 0.7844461581951896 1.0 0.5 3.069089109365284
48.0 0.3195541476806115 1.0 0.5 0.7700140609818293
49.0 0.326892158146161 1.0 0.5 0.7916994433570004
50.0 0.4392312327086285 1.0 0.5 1.1568932758900772
51.0 0.5377790694946909 1.0 0.5 1.543424595293625
52.0 0.4369640582174875 1.0 0.5 1.1488236262486446
53.0 0.26672242876690055 1.0 0.5 0.6204619408451196
54.0 0.9743181848790359 1.0 0.5 7.323944240755433
55.0 0.5636877255447679 1.0 0.5 1.6587941323713102
56.0 0.8214194684040824 1.0 0.5 3.44543124420649
57.0 4.2394218638494574e-2 1.0 0.5 8.663817482333575e-2
58.0 0.2986030735782996 1.0 0.5 0.7093626466953578
59.0 0.9251464009715654 1.0 0.5 5.184442172120483
60.0 0.9768531076059933 1.0 0.5 7.531789490600966
61.0 0.4147651110232632 1.0 0.5 1.0714839854387161
62.0 0.4525161010109643 1.0 0.5 1.2048444519262322
63.0 7.638776464132979e-2 1.0 0.5 0.1589259082490955
64.0 0.8203900440907219 1.0 0.5 3.433935381714252
65.0 0.9746746584977457 1.0 0.5 7.35189948830076
66.0 0.41832172801299305 1.0 0.5 1.083675562745256
67.0 3.3131200470495226e-2 1.0 0.5 6.738494114620364e-2
68.0 0.10008247055930286 1.0 0.5 0.21090430762250917
69.0 0.4268021831375646 1.0 0.5 1.113048783438383
70.0 0.8213380254753332 1.0 0.5 3.444519337826204
71.0 0.47431121070064797 1.0 0.5 1.2860917933318652
72.0 0.68679164992865 1.0 0.5 2.321773309424188
73.0 0.7057803676609208 1.0 0.5 2.4468574835462356
74.0 0.32184620342731496 1.0 0.5 0.776762356325894
75.0 0.3589329148022541 1.0 0.5 0.8892423408857425
76.0 0.7448782338623747 1.0 0.5 2.7320286670643386
77.0 0.9740613004640858 1.0 0.5 7.304038469785621
78.0 0.7453909609063684 1.0 0.5 2.736052180743762
79.0 6.853610233988816e-2 1.0 0.5 0.14199569380051374
80.0 0.336012781812836 1.0 0.5 0.8189847588182159
81.0 0.2963058480260412 1.0 0.5 0.7028229208813994
82.0 0.38627232525200883 1.0 0.5 0.9764079513820425
83.0 0.9097248909817963 1.0 0.5 4.809787008391862
84.0 0.20679745942261907 1.0 0.5 0.46335335878970363
85.0 0.16582497569469312 1.0 0.5 0.36262407472768277
86.0 0.6960738838737711 1.0 0.5 2.381941292346302
87.0 0.890094879396298 1.0 0.5 4.416275650715409
88.0 0.8258738496535992 1.0 0.5 3.4959504809275685
89.0 0.4066244237870885 1.0 0.5 1.0438554620679272
90.0 0.44414816275414526 1.0 0.5 1.1745070000344822
91.0 0.8820223175378497 1.0 0.5 4.274519608161631
92.0 0.3814200182827251 1.0 0.5 0.9606575597598919
93.0 0.491252177347836 1.0 0.5 1.3516056440673538
94.0 0.9042145561359308 1.0 0.5 4.691289097027222
95.0 0.8293982814391448 1.0 0.5 3.536847140695551
96.0 0.6957817964411346 1.0 0.5 2.38002012037681
97.0 0.46108317902841456 1.0 0.5 1.2363880819986401
98.0 0.658234439306857 1.0 0.5 2.14726054405596
99.0 0.43175037735005384 1.0 0.5 1.130388960612226
100.0 0.7719881477151886 1.0 0.5 2.9567153353469786
101.0 6.397418621476536e-2 1.0 0.5 0.13222444810891013
102.0 0.44410081132020296 1.0 0.5 1.1743366329905425
103.0 0.9364231799229901 1.0 0.5 5.511012678534471
104.0 0.5453471566845608 1.0 0.5 1.576442265948382
105.0 0.7346238968987211 1.0 0.5 2.653214404406468
106.0 0.3493365535175731 1.0 0.5 0.8595254994862054
107.0 0.5230037795263933 1.0 0.5 1.480493423321206
108.0 0.6886814284788837 1.0 0.5 2.333877090719847
109.0 0.7731252946239237 1.0 0.5 2.966714745163421
110.0 2.276168830750991e-2 1.0 0.5 4.604946957472576e-2
111.0 0.264951110753621 1.0 0.5 0.6156365319998442
112.0 0.14616140102686104 1.0 0.5 0.3160261944637388
113.0 3.066619523108849e-2 1.0 0.5 6.229248529326732e-2
114.0 0.49017052188807597 1.0 0.5 1.3473579316333943
115.0 9.835381148010536e-2 1.0 0.5 0.20706617613153588
116.0 8.828156810764243e-2 1.0 0.5 0.1848481470740138
117.0 0.6868446103815881 1.0 0.5 2.3221115183574854
118.0 0.4067862578001439 1.0 0.5 1.0444010055396156
119.0 0.44070042328022496 1.0 0.5 1.1621400679168603
120.0 0.19523663294276805 1.0 0.5 0.4344139974853618
121.0 0.34930320794183467 1.0 0.5 0.8594230049585315
122.0 0.37713232784782635 1.0 0.5 0.9468423740115679
123.0 0.6429635193876022 1.0 0.5 2.0598346316676848
124.0 0.5726782020473655 1.0 0.5 1.7004358488091253
125.0 0.3013872989669776 1.0 0.5 0.7173175321607891
126.0 0.3469657736553403 1.0 0.5 0.8522514741503977
127.0 0.3062597218624077 1.0 0.5 0.7313152550300903
128.0 0.875187814442521 1.0 0.5 4.161890374256847
129.0 0.4331447487608374 1.0 0.5 1.1353025933318837
130.0 0.40669672646934574 1.0 0.5 1.0440991764725864
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965.0 0.5756726043081537 1.0 0.5 1.714499924122977
966.0 0.14180795869433915 1.0 0.5 0.3058547603470779
967.0 0.476602852426136 1.0 0.5 1.2948294774050015
968.0 0.5735933728030692 1.0 0.5 1.7047237280891907
969.0 0.21074148987963792 1.0 0.5 0.47332273812264397
970.0 0.4040283383810781 1.0 0.5 1.0351243213329395
971.0 0.44809616679520103 1.0 0.5 1.188762926181943
972.0 0.49753260138877997 1.0 0.5 1.376449039078463
973.0 0.3981895324367999 1.0 0.5 1.0156254423601343
974.0 0.4631341447354761 1.0 0.5 1.2440140393123216
975.0 0.7621220718869883 1.0 0.5 2.8719952879613677
976.0 0.35491286990322435 1.0 0.5 0.8767397717764418
977.0 0.5624416059435056 1.0 0.5 1.6530902199238997
978.0 0.9048958001682184 1.0 0.5 4.705564296273839
979.0 0.5871353426885598 1.0 0.5 1.769270891992473
980.0 0.9552974642377905 1.0 0.5 6.215450101021099
981.0 0.11683294268351829 1.0 0.5 0.24848180677799192
982.0 0.804763553103361 1.0 0.5 3.2670878135466657
983.0 0.9017746463190758 1.0 0.5 4.640981825644075
984.0 0.3546593618234335 1.0 0.5 0.8759539607786164
985.0 0.8175329055993971 1.0 0.5 3.4023708537413193
986.0 0.9271651336840998 1.0 0.5 5.239121011041082
987.0 0.43755514801054285 1.0 0.5 1.150924381235035
988.0 0.12335439229044076 1.0 0.5 0.2633049287820745
989.0 0.3823717678509384 1.0 0.5 0.9637371372795477
990.0 0.7134192888551714 1.0 0.5 2.499470136417535
991.0 0.5559806916407091 1.0 0.5 1.6237744603995141
992.0 0.7947950806945909 1.0 0.5 3.167492385499269
993.0 0.8593443260366468 1.0 0.5 3.9228808076956767
994.0 0.9695468897099642 1.0 0.5 6.983134291741286
995.0 9.645307355937993e-2 1.0 0.5 0.20285446358422873
996.0 0.5759218175673997 1.0 0.5 1.7156748964373492
997.0 0.8948271404741518 1.0 0.5 4.504300002523024
998.0 0.8288317043606008 1.0 0.5 3.5302160428926017
999.0 0.7727026977235016 1.0 0.5 2.962992833506503
dfExpRand.describe().show() // look sensible
+-------+-----------------+--------------------+----+----+--------------------+
|summary|               Id|                rand| one|rate|         expo_sample|
+-------+-----------------+--------------------+----+----+--------------------+
|  count|             1000|                1000|1000|1000|                1000|
|   mean|            499.5|  0.5060789944940257| 1.0| 0.5|   2.024647367046763|
| stddev|288.8194360957494| 0.28795893414434537| 0.0| 0.0|  1.9649069025265538|
|    min|                0|6.282087728304298E-4| 1.0| 0.5|0.001256812357281...|
|    max|              999|  0.9981606891187609| 1.0| 0.5|  12.596728597154938|
+-------+-----------------+--------------------+----+----+--------------------+
val expoSamplesDF = spark.range(1000000000).toDF("Id") // just make a DF of 100 row indices
               .select($"Id", rand(seed=1234567) as "rand") // add a column of random numbers in (0,1)
               .withColumn("one",lit(1.0))
               .withColumn("rate",lit(0.5))
               .withColumn("expo_sample", -($"one" / $"rate") * log($"one" - $"rand"))
expoSamplesDF: org.apache.spark.sql.DataFrame = [Id: bigint, rand: double ... 3 more fields]
expoSamplesDF.describe().show()
+-------+--------------------+--------------------+----------+----------+--------------------+
|summary|                  Id|                rand|       one|      rate|         expo_sample|
+-------+--------------------+--------------------+----------+----------+--------------------+
|  count|          1000000000|          1000000000|1000000000|1000000000|          1000000000|
|   mean|4.9999999907595944E8| 0.49999521358240573|       1.0|       0.5|  1.9999814119383708|
| stddev|2.8867513473915565E8|  0.2886816216562552|       0.0|       0.0|  2.0000011916404206|
|    min|                   0|1.584746778249268...|       1.0|       0.5|3.169493556749679...|
|    max|           999999999|  0.9999999996809935|       1.0|       0.5|  43.731619350261035|
+-------+--------------------+--------------------+----------+----------+--------------------+

Approximating Pi with Monte Carlo simulations

Uisng RDDs directly, let's estimate Pi.

//Calculate pi with Monte Carlo estimation
import scala.math.random

//make a very large unique set of 1 -> n 
val partitions = 2 
val n = math.min(100000L * partitions, Int.MaxValue).toInt 
val xs = 1 until n 

//split up n into the number of partitions we can use 
val rdd = sc.parallelize(xs, partitions).setName("'N values rdd'")

//generate a random set of points within a 2x2 square
val sample = rdd.map { i =>
  val x = random * 2 - 1
  val y = random * 2 - 1
  (x, y)
}.setName("'Random points rdd'")

//points w/in the square also w/in the center circle of r=1
val inside = sample.filter { case (x, y) => (x * x + y * y < 1) }.setName("'Random points inside circle'")
val count = inside.count()
 
//Area(circle)/Area(square) = inside/n => pi=4*inside/n                        
println("Pi is roughly " + 4.0 * count / n)
Pi is roughly 3.14156
import scala.math.random
partitions: Int = 2
n: Int = 200000
xs: scala.collection.immutable.Range = Range 1 until 200000
rdd: org.apache.spark.rdd.RDD[Int] = 'N values rdd' ParallelCollectionRDD[39] at parallelize at command-2971213210276568:10
sample: org.apache.spark.rdd.RDD[(Double, Double)] = 'Random points rdd' MapPartitionsRDD[40] at map at command-2971213210276568:13
inside: org.apache.spark.rdd.RDD[(Double, Double)] = 'Random points inside circle' MapPartitionsRDD[41] at filter at command-2971213210276568:20
count: Long = 157078

Doing it in PySpark is just as easy. This may be needed if there are pyhton libraries you want to take advantage of in Spark.

# # Estimating $\pi$
#
# This PySpark example shows you how to estimate $\pi$ in parallel
# using Monte Carlo integration.

from __future__ import print_function
import sys
from random import random
from operator import add

partitions = 2
n = 100000 * partitions

def f(_):
    x = random() * 2 - 1
    y = random() * 2 - 1
    return 1 if x ** 2 + y ** 2 < 1 else 0

# To access the associated SparkContext
count = spark.sparkContext.parallelize(range(1, n + 1), partitions).map(f).reduce(add)
print("Pi is roughly %f" % (4.0 * count / n))
Pi is roughly 3.138820

The following is from this google turotial.

Programming a Monte Carlo simulation in Scala

Monte Carlo, of course, is famous as a gambling destination. In this section, you use Scala to create a simulation that models the mathematical advantage that a casino enjoys in a game of chance. The "house edge" at a real casino varies widely from game to game; it can be over 20% in keno, for example. This tutorial creates a simple game where the house has only a one-percent advantage. Here's how the game works:

  1. The player places a bet, consisting of a number of chips from a bankroll fund.
  • The player rolls a 100-sided die (how cool would that be?).
  • If the result of the roll is a number from 1 to 49, the player wins.
  • For results 50 to 100, the player loses the bet.

You can see that this game creates a one-percent disadvantage for the player: in 51 of the 100 possible outcomes for each roll, the player loses.

Follow these steps to create and run the game:

val STARTING_FUND = 10
val STAKE = 1   // the amount of the bet
val NUMBER_OF_GAMES = 25

def rollDie: Int = {
    val r = scala.util.Random
    r.nextInt(99) + 1
}

def playGame(stake: Int): (Int) = {
    val faceValue = rollDie
    if (faceValue < 50)
        (2*stake)
    else
        (0)
}

// Function to play the game multiple times
// Returns the final fund amount
def playSession(
   startingFund: Int = STARTING_FUND,
   stake: Int = STAKE,
   numberOfGames: Int = NUMBER_OF_GAMES):
   (Int) = {

    // Initialize values
    var (currentFund, currentStake, currentGame) = (startingFund, 0, 1)

    // Keep playing until number of games is reached or funds run out
    while (currentGame <= numberOfGames && currentFund > 0) {

        // Set the current bet and deduct it from the fund
        currentStake = math.min(stake, currentFund)
        currentFund -= currentStake

        // Play the game
        val (winnings) = playGame(currentStake)

        // Add any winnings
        currentFund += winnings

        // Increment the loop counter
        currentGame += 1
    }
    (currentFund)
}
STARTING_FUND: Int = 10
STAKE: Int = 1
NUMBER_OF_GAMES: Int = 25
rollDie: Int
playGame: (stake: Int)Int
playSession: (startingFund: Int, stake: Int, numberOfGames: Int)Int

Enter the following code to play the game 25 times, which is the default value for NUMBER_OF_GAMES.

playSession()
res31: Int = 5

Your bankroll started with a value of 10 units. Is it higher or lower, now?

Now simulate 10,000 players betting 100 chips per game. Play 10,000 games in a session. This Monte Carlo simulation calculates the probability of losing all your money before the end of the session. Enter the follow code:

(sc.parallelize(1 to 10000, 500)
  .map(i => playSession(100000, 100, 250000))
  .map(i => if (i == 0) 1 else 0)
  .reduce(_+_)/10000.0)
res32: Double = 0.9992

Note that the syntax .reduce(_+_) is shorthand in Scala for aggregating by using a summing function.

The preceding code performs the following steps:

  1. Creates an RDD with the results of playing the session.
  • Replaces bankrupt players' results with the number 1 and nonzero results with the number 0.
  • Sums the count of bankrupt players.
  • Divides the count by the number of players.

A typical result might be:

res32: Double = 0.9992

Which represents a near guarantee of losing all your money, even though the casino had only a one-percent advantage.

Project Ideas

Try to create a scalable simulation of interest to you.

Here are some mature projects:

  • https://github.com/zishanfu/GeoSparkSim
  • https://github.com/srbaird/mc-var-spark

See a more complete VaR modeling: - https://databricks.com/blog/2020/05/27/modernizing-risk-management-part-1-streaming-data-ingestion-rapid-model-development-and-monte-carlo-simulations-at-scale.html

ScaDaMaLe Course site and book

Introduction to Machine Learning

Some very useful resources we will weave around for Statistical Learning, Data Mining, Machine Learning:

Deep Learning is a very popular method currently (2017) in Machine Learning and I recommend Andrew Ng's free course in Courseera for this if you have not taken a course in deep learning already.

Note: This is an applied course in data science and we will quickly move to doing things with data. You have to do work to get a deeper mathematical understanding or take other courses. We will focus on intution here and the distributed ML Pipeline in action.

I am assuming several of you have or are taking ML courses. In this course we will focus on getting our hads dirty quickly with some level of common understanding across all the disciplines represented here. Please dive deep at your own time to desired depths and tangents based on your background.

Summary of Machine Learning at a High Level

  • A rough definition of machine learning.
    • constructing and studying algorithms that learn from and make predictions on data.
  • This broad area involves tools and ideas from various domains, including:
    • computer science,
    • probability and statistics,
    • optimization,
    • linear algebra
    • logic
    • etc.
  • Common examples of ML, include:
    • facial recognition,
    • link prediction,
    • text or document classification, eg.::
      • spam detection,
    • protein structure prediction
    • teaching computers to play games (go!)

Some common terminology

using example of spam detection as a running example.
  • the data points we learn from are call observations:

    • they are items or entities used for::
      • learning or
      • evaluation.
  • in the context of spam detection,

    • emails are our observations.
    • Features are attributes used to represent an observation.
    • Features are typically numeric,
      • and in spam detection, they can be:
      • the length,
      • the date, or
      • the presence or absence of keywords in emails.
    • Labels are values or categories assigned to observations.
      • and in spam detection, they can be:
      • an email being defined as spam or not spam.
  • Training and test data sets are the observations that we use to train and evaluate a learning algorithm.

  • Pop-Quiz

    • What is the difference between supervised and unsupervised learning?

ML Pipelines

Here we will use ML Pipelines to do machine learning at scale.

See https://spark.apache.org/docs/latest/ml-pipeline.html for a quick overview.

Read this section for an overview:

ScaDaMaLe Course site and book

Million Song Dataset - Kaggle Challenge

Predict which songs a user will listen to.

SOURCE: This is just a Scala-rification of the Python notebook published in databricks community edition in 2016.

When you first hear a song, do you ever categorize it as slow or fast in your head? Is it even a valid categorization? If so, can one do it automatically? I have always wondered about that. That is why I got excited when I learned about the Million Songs Dataset -Kaggle Challenge.

In this tutorial we will walk through a practical example of a data science project with Apache Spark in Python. We are going to parse, explore and model a sample from the million songs dataset stored on distributed storage. This tutorial is organized into three sections:

  1. ETL: Parses raw texts and creates a cached table
  2. Explore: Explores different aspects of the songs table using graphs
  3. Model: Uses SparkML to cluster songs based on some of their attributes

End to End Data Science

The goal of this tutorial is to prepare you for real world data science projects. Make sure you go through the tutorial in the above order and use the exercises to make yourself familiar further with the API. Also make sure you run these notebooks on a 1.6.x cluster.

1. ETL

The first step of most data science projects is extracting, transforming and loading data into well formated tables. Our example starts with ETL as well. By following the ETL noteboook you can expect to learn about following Spark concepts:

  • RDD: Resilient Distributed Dataset
  • Reading and transforming RDDs
  • Schema in Spark
  • Spark DataFrame
  • Temp tables
  • Caching tables

2. Explore

Exploratory analysis is a key step in any real data project. Data scientists use variety of tools to explore and visualize their data. In the second notebook of this tutorial we introduce several tools in Python and Databricks notebooks that can help you visually explore your large data. By reading this notebook and finishing its exercises you will become familiar with:

  • How to view the schema of a table
  • How to display ggplot and matplotlib figures in Notebooks
  • How to summarize and visualize different aspects of large datasets
  • How to sample and visualize large data

3. Model

The end goal of many data scientists is producing useful models. These models are often used for prediction of new and upcoming events in production. In our third notebook we construct a simple K-means clustering model. In this notebook you will learn about:

  • Feature transformation
  • Fitting a model using SparkML API
  • Applying a model to data
  • Visualizing model results
  • Model tuning

ScaDaMaLe Course site and book

Million Song Dataset - Kaggle Challenge

Predict which songs a user will listen to.

SOURCE: This is just a Scala-rification of the Python notebook published in databricks community edition in 2016.

CAUTION: This notebook is expected to have an error in command 28 (Cmd 28 in databricks notebook). You are meant to learn how to fix this error with simple exception-handling to become a better data scientist. So ignore this warning, if any.

Stage 1: Parsing songs data

ETL

This is the first notebook in this tutorial. In this notebook we will read data from DBFS (DataBricks FileSystem). We will parse data and load it as a table that can be readily used in following notebooks.

By going through this notebook you can expect to learn how to read distributed data as an RDD, how to transform RDDs, and how to construct a Spark DataFrame from an RDD and register it as a table.

We first explore different files in our distributed file system. We use a header file to construct a Spark Schema object. We write a function that takes the header and casts strings in each line of our data to corresponding types. Once we run this function on the data we find that it fails on some corner caes. We update our function and finally get a parsed RDD. We combine that RDD and the Schema to construct a DataFame and register it as a temporary table in SparkSQL.

Text data files are stored in dbfs:/databricks-datasets/songs/data-001

You can conveniently list files on distributed file system (DBFS, S3 or HDFS) using %fs commands.

ls /databricks-datasets/songs/data-001/
path name size
dbfs:/databricks-datasets/songs/data-001/header.txt header.txt 377.0
dbfs:/databricks-datasets/songs/data-001/part-00000 part-00000 52837.0
dbfs:/databricks-datasets/songs/data-001/part-00001 part-00001 52469.0
dbfs:/databricks-datasets/songs/data-001/part-00002 part-00002 51778.0
dbfs:/databricks-datasets/songs/data-001/part-00003 part-00003 50551.0
dbfs:/databricks-datasets/songs/data-001/part-00004 part-00004 53449.0
dbfs:/databricks-datasets/songs/data-001/part-00005 part-00005 53301.0
dbfs:/databricks-datasets/songs/data-001/part-00006 part-00006 54184.0
dbfs:/databricks-datasets/songs/data-001/part-00007 part-00007 50924.0
dbfs:/databricks-datasets/songs/data-001/part-00008 part-00008 52533.0
dbfs:/databricks-datasets/songs/data-001/part-00009 part-00009 54570.0
dbfs:/databricks-datasets/songs/data-001/part-00010 part-00010 54338.0
dbfs:/databricks-datasets/songs/data-001/part-00011 part-00011 51836.0
dbfs:/databricks-datasets/songs/data-001/part-00012 part-00012 52297.0
dbfs:/databricks-datasets/songs/data-001/part-00013 part-00013 52044.0
dbfs:/databricks-datasets/songs/data-001/part-00014 part-00014 50704.0
dbfs:/databricks-datasets/songs/data-001/part-00015 part-00015 54158.0
dbfs:/databricks-datasets/songs/data-001/part-00016 part-00016 50080.0
dbfs:/databricks-datasets/songs/data-001/part-00017 part-00017 47708.0
dbfs:/databricks-datasets/songs/data-001/part-00018 part-00018 8858.0
dbfs:/databricks-datasets/songs/data-001/part-00019 part-00019 53323.0
dbfs:/databricks-datasets/songs/data-001/part-00020 part-00020 57877.0
dbfs:/databricks-datasets/songs/data-001/part-00021 part-00021 52491.0
dbfs:/databricks-datasets/songs/data-001/part-00022 part-00022 54791.0
dbfs:/databricks-datasets/songs/data-001/part-00023 part-00023 50682.0
dbfs:/databricks-datasets/songs/data-001/part-00024 part-00024 52863.0
dbfs:/databricks-datasets/songs/data-001/part-00025 part-00025 47416.0
dbfs:/databricks-datasets/songs/data-001/part-00026 part-00026 50130.0
dbfs:/databricks-datasets/songs/data-001/part-00027 part-00027 53462.0
dbfs:/databricks-datasets/songs/data-001/part-00028 part-00028 54179.0
dbfs:/databricks-datasets/songs/data-001/part-00029 part-00029 52738.0
dbfs:/databricks-datasets/songs/data-001/part-00030 part-00030 54159.0
dbfs:/databricks-datasets/songs/data-001/part-00031 part-00031 51247.0
dbfs:/databricks-datasets/songs/data-001/part-00032 part-00032 51610.0
dbfs:/databricks-datasets/songs/data-001/part-00033 part-00033 53895.0
dbfs:/databricks-datasets/songs/data-001/part-00034 part-00034 53125.0
dbfs:/databricks-datasets/songs/data-001/part-00035 part-00035 54066.0
dbfs:/databricks-datasets/songs/data-001/part-00036 part-00036 54265.0
dbfs:/databricks-datasets/songs/data-001/part-00037 part-00037 54264.0
dbfs:/databricks-datasets/songs/data-001/part-00038 part-00038 50540.0
dbfs:/databricks-datasets/songs/data-001/part-00039 part-00039 55193.0
dbfs:/databricks-datasets/songs/data-001/part-00040 part-00040 54537.0
dbfs:/databricks-datasets/songs/data-001/part-00041 part-00041 52402.0
dbfs:/databricks-datasets/songs/data-001/part-00042 part-00042 54673.0
dbfs:/databricks-datasets/songs/data-001/part-00043 part-00043 53009.0
dbfs:/databricks-datasets/songs/data-001/part-00044 part-00044 51789.0
dbfs:/databricks-datasets/songs/data-001/part-00045 part-00045 52986.0
dbfs:/databricks-datasets/songs/data-001/part-00046 part-00046 54442.0
dbfs:/databricks-datasets/songs/data-001/part-00047 part-00047 52971.0
dbfs:/databricks-datasets/songs/data-001/part-00048 part-00048 53331.0
dbfs:/databricks-datasets/songs/data-001/part-00049 part-00049 44263.0
dbfs:/databricks-datasets/songs/data-001/part-00050 part-00050 54841.0
dbfs:/databricks-datasets/songs/data-001/part-00051 part-00051 54306.0
dbfs:/databricks-datasets/songs/data-001/part-00052 part-00052 53610.0
dbfs:/databricks-datasets/songs/data-001/part-00053 part-00053 53573.0
dbfs:/databricks-datasets/songs/data-001/part-00054 part-00054 53854.0
dbfs:/databricks-datasets/songs/data-001/part-00055 part-00055 54236.0
dbfs:/databricks-datasets/songs/data-001/part-00056 part-00056 54455.0
dbfs:/databricks-datasets/songs/data-001/part-00057 part-00057 52307.0
dbfs:/databricks-datasets/songs/data-001/part-00058 part-00058 52313.0
dbfs:/databricks-datasets/songs/data-001/part-00059 part-00059 52446.0
dbfs:/databricks-datasets/songs/data-001/part-00060 part-00060 51958.0
dbfs:/databricks-datasets/songs/data-001/part-00061 part-00061 53859.0
dbfs:/databricks-datasets/songs/data-001/part-00062 part-00062 53698.0
dbfs:/databricks-datasets/songs/data-001/part-00063 part-00063 54482.0
dbfs:/databricks-datasets/songs/data-001/part-00064 part-00064 40182.0
dbfs:/databricks-datasets/songs/data-001/part-00065 part-00065 54410.0
dbfs:/databricks-datasets/songs/data-001/part-00066 part-00066 49123.0
dbfs:/databricks-datasets/songs/data-001/part-00067 part-00067 50796.0
dbfs:/databricks-datasets/songs/data-001/part-00068 part-00068 49561.0
dbfs:/databricks-datasets/songs/data-001/part-00069 part-00069 52294.0
dbfs:/databricks-datasets/songs/data-001/part-00070 part-00070 51250.0
dbfs:/databricks-datasets/songs/data-001/part-00071 part-00071 58942.0
dbfs:/databricks-datasets/songs/data-001/part-00072 part-00072 54589.0
dbfs:/databricks-datasets/songs/data-001/part-00073 part-00073 54233.0
dbfs:/databricks-datasets/songs/data-001/part-00074 part-00074 54725.0
dbfs:/databricks-datasets/songs/data-001/part-00075 part-00075 54877.0
dbfs:/databricks-datasets/songs/data-001/part-00076 part-00076 54333.0
dbfs:/databricks-datasets/songs/data-001/part-00077 part-00077 51927.0
dbfs:/databricks-datasets/songs/data-001/part-00078 part-00078 51744.0
dbfs:/databricks-datasets/songs/data-001/part-00079 part-00079 53187.0
dbfs:/databricks-datasets/songs/data-001/part-00080 part-00080 43246.0
dbfs:/databricks-datasets/songs/data-001/part-00081 part-00081 54269.0
dbfs:/databricks-datasets/songs/data-001/part-00082 part-00082 48464.0
dbfs:/databricks-datasets/songs/data-001/part-00083 part-00083 52144.0
dbfs:/databricks-datasets/songs/data-001/part-00084 part-00084 53375.0
dbfs:/databricks-datasets/songs/data-001/part-00085 part-00085 55139.0
dbfs:/databricks-datasets/songs/data-001/part-00086 part-00086 50924.0
dbfs:/databricks-datasets/songs/data-001/part-00087 part-00087 52013.0
dbfs:/databricks-datasets/songs/data-001/part-00088 part-00088 54262.0
dbfs:/databricks-datasets/songs/data-001/part-00089 part-00089 53007.0
dbfs:/databricks-datasets/songs/data-001/part-00090 part-00090 55142.0
dbfs:/databricks-datasets/songs/data-001/part-00091 part-00091 52049.0
dbfs:/databricks-datasets/songs/data-001/part-00092 part-00092 54714.0
dbfs:/databricks-datasets/songs/data-001/part-00093 part-00093 52906.0
dbfs:/databricks-datasets/songs/data-001/part-00094 part-00094 52188.0
dbfs:/databricks-datasets/songs/data-001/part-00095 part-00095 50768.0
dbfs:/databricks-datasets/songs/data-001/part-00096 part-00096 55242.0
dbfs:/databricks-datasets/songs/data-001/part-00097 part-00097 52059.0
dbfs:/databricks-datasets/songs/data-001/part-00098 part-00098 52982.0
dbfs:/databricks-datasets/songs/data-001/part-00099 part-00099 52015.0
dbfs:/databricks-datasets/songs/data-001/part-00100 part-00100 51467.0
dbfs:/databricks-datasets/songs/data-001/part-00101 part-00101 50926.0
dbfs:/databricks-datasets/songs/data-001/part-00102 part-00102 55018.0
dbfs:/databricks-datasets/songs/data-001/part-00103 part-00103 50043.0
dbfs:/databricks-datasets/songs/data-001/part-00104 part-00104 51936.0
dbfs:/databricks-datasets/songs/data-001/part-00105 part-00105 57311.0
dbfs:/databricks-datasets/songs/data-001/part-00106 part-00106 55090.0
dbfs:/databricks-datasets/songs/data-001/part-00107 part-00107 54396.0
dbfs:/databricks-datasets/songs/data-001/part-00108 part-00108 56594.0
dbfs:/databricks-datasets/songs/data-001/part-00109 part-00109 53260.0
dbfs:/databricks-datasets/songs/data-001/part-00110 part-00110 42007.0
dbfs:/databricks-datasets/songs/data-001/part-00119 part-00119 0.0

As you can see in the listing we have data files and a single header file. The header file seems interesting and worth a first inspection at first. The file is 377 bytes, therefore it is safe to collect the entire content of the file in the notebook.

sc.textFile("databricks-datasets/songs/data-001/header.txt").collect() 
res1: Array[String] = Array(artist_id:string, artist_latitude:double, artist_longitude:double, artist_location:string, artist_name:string, duration:double, end_of_fade_in:double, key:int, key_confidence:double, loudness:double, release:string, song_hotnes:double, song_id:string, start_of_fade_out:double, tempo:double, time_signature:double, time_signature_confidence:double, title:string, year:double, partial_sequence:int)

Remember you can collect() a huge RDD and crash the driver program - so it is a good practise to take a couple lines and count the number of lines, especially if you have no idea what file you are trying to read.

sc.textFile("databricks-datasets/songs/data-001/header.txt").take(2)
res2: Array[String] = Array(artist_id:string, artist_latitude:double)
sc.textFile("databricks-datasets/songs/data-001/header.txt").count()
res3: Long = 20
sc.textFile("databricks-datasets/songs/data-001/header.txt").collect.map(println) // uncomment to see line-by-line
artist_id:string
artist_latitude:double
artist_longitude:double
artist_location:string
artist_name:string
duration:double
end_of_fade_in:double
key:int
key_confidence:double
loudness:double
release:string
song_hotnes:double
song_id:string
start_of_fade_out:double
tempo:double
time_signature:double
time_signature_confidence:double
title:string
year:double
partial_sequence:int
res4: Array[Unit] = Array((), (), (), (), (), (), (), (), (), (), (), (), (), (), (), (), (), (), (), ())

As seen above each line in the header consists of a name and a type separated by colon. We will need to parse the header file as follows:

val header = sc.textFile("/databricks-datasets/songs/data-001/header.txt").map(
      line => {
                val headerElement = line.split(":")
                (headerElement(0), headerElement(1))
            }
           ).collect()
header: Array[(String, String)] = Array((artist_id,string), (artist_latitude,double), (artist_longitude,double), (artist_location,string), (artist_name,string), (duration,double), (end_of_fade_in,double), (key,int), (key_confidence,double), (loudness,double), (release,string), (song_hotnes,double), (song_id,string), (start_of_fade_out,double), (tempo,double), (time_signature,double), (time_signature_confidence,double), (title,string), (year,double), (partial_sequence,int))

Let's define a case class called Song that will be used to represent each row of data in the files:

  • /databricks-datasets/songs/data-001/part-00000 through /databricks-datasets/songs/data-001/part-00119 or the last .../part-***** file.
case class Song(artist_id: String, artist_latitude: Double, artist_longitude: Double, artist_location: String, artist_name: String, duration: Double, end_of_fade_in: Double, key: Int, key_confidence: Double, loudness: Double, release: String, song_hotness: Double, song_id: String, start_of_fade_out: Double, tempo: Double, time_signature: Double, time_signature_confidence: Double, title: String, year: Double, partial_sequence: Int)
defined class Song

Now we turn to data files. First, step is inspecting the first line of data to inspect its format.

// this is loads all the data - a subset of the 1M songs dataset
val dataRDD = sc.textFile("/databricks-datasets/songs/data-001/part-*") 
dataRDD: org.apache.spark.rdd.RDD[String] = /databricks-datasets/songs/data-001/part-* MapPartitionsRDD[54] at textFile at command-2971213210276292:2
dataRDD.count // number of songs
res5: Long = 31369
dataRDD.take(3)
res6: Array[String] = Array(AR81V6H1187FB48872	nan	nan		Earl Sixteen	213.7073	0.0	11	0.419	-12.106	Soldier of Jah Army	nan	SOVNZSZ12AB018A9B8	208.289	125.882	1	0.0	Rastaman	2003	--, ARVVZQP11E2835DBCB	nan	nan		Wavves	133.25016	0.0	0	0.282	0.596	Wavvves	0.471578247701	SOJTQHQ12A8C143C5F	128.116	89.519	1	0.0	I Want To See You (And Go To The Movies)	2009	--, ARFG9M11187FB3BBCB	nan	nan	Nashua USA	C-Side	247.32689	0.0	9	0.612	-4.896	Santa Festival Compilation 2008 vol.1	nan	SOAJSQL12AB0180501	242.196	171.278	5	1.0	Loose on the Dancefloor	0	225261)

Each line of data consists of multiple fields separated by \t. With that information and what we learned from the header file, we set out to parse our data.

  • We have already created a case class based on the header (which seems to agree with the 3 lines above).
  • Next, we will create a function that takes each line as input and returns the case class as output.
// let's do this 'by hand' to re-flex our RDD-muscles :)
// although this is not a robust way to read from a data engineering perspective (without fielding exceptions)
def parseLine(line: String): Song = {
  
  val tokens = line.split("\t")
  Song(tokens(0), tokens(1).toDouble, tokens(2).toDouble, tokens(3), tokens(4), tokens(5).toDouble, tokens(6).toDouble, tokens(7).toInt, tokens(8).toDouble, tokens(9).toDouble, tokens(10), tokens(11).toDouble, tokens(12), tokens(13).toDouble, tokens(14).toDouble, tokens(15).toDouble, tokens(16).toDouble, tokens(17), tokens(18).toDouble, tokens(19).toInt)
}
parseLine: (line: String)Song

With this function we can transform the dataRDD to another RDD that consists of Song case classes

val parsedRDD = dataRDD.map(parseLine)
parsedRDD: org.apache.spark.rdd.RDD[Song] = MapPartitionsRDD[55] at map at command-2971213210276298:1

To convert an RDD of case classes to a DataFrame, we just need to call the toDF method

val df = parsedRDD.toDF
df: org.apache.spark.sql.DataFrame = [artist_id: string, artist_latitude: double ... 18 more fields]

Once we get a DataFrame we can register it as a temporary table. That will allow us to use its name in SQL queries.

df.createOrReplaceTempView("songsTable")

We can now cache our table. So far all operations have been lazy. This is the first time Spark will attempt to actually read all our data and apply the transformations.

If you are running Spark 1.6+ the next command will throw a parsing error.

cache table songsTable

The error means that we are trying to convert a missing value to a Double. Here is an updated version of the parseLine function to deal with missing values

// good data engineering science practise
def parseLine(line: String): Song = {
  
  
  def toDouble(value: String, defaultVal: Double): Double = {
    try {
       value.toDouble
    } catch {
      case e: Exception => defaultVal
    }
  }

  def toInt(value: String, defaultVal: Int): Int = {
    try {
       value.toInt
      } catch {
      case e: Exception => defaultVal
    }
  }
  
  val tokens = line.split("\t")
  Song(tokens(0), toDouble(tokens(1), 0.0), toDouble(tokens(2), 0.0), tokens(3), tokens(4), toDouble(tokens(5), 0.0), toDouble(tokens(6), 0.0), toInt(tokens(7), -1), toDouble(tokens(8), 0.0), toDouble(tokens(9), 0.0), tokens(10), toDouble(tokens(11), 0.0), tokens(12), toDouble(tokens(13), 0.0), toDouble(tokens(14), 0.0), toDouble(tokens(15), 0.0), toDouble(tokens(16), 0.0), tokens(17), toDouble(tokens(18), 0.0), toInt(tokens(19), -1))
}
parseLine: (line: String)Song
val df = dataRDD.map(parseLine).toDF
df.createOrReplaceTempView("songsTable")
df: org.apache.spark.sql.DataFrame = [artist_id: string, artist_latitude: double ... 18 more fields]

And let's try caching the table. We are going to access this data multiple times in following notebooks, therefore it is a good idea to cache it in memory for faster subsequent access.

cache table songsTable

From now on we can easily query our data using the temporary table we just created and cached in memory. Since it is registered as a table we can conveniently use SQL as well as Spark API to access it.

select * from songsTable limit 10
artist_id artist_latitude artist_longitude artist_location artist_name duration end_of_fade_in key key_confidence loudness release song_hotness song_id start_of_fade_out tempo time_signature time_signature_confidence title year partial_sequence
AR81V6H1187FB48872 0.0 0.0 Earl Sixteen 213.7073 0.0 11.0 0.419 -12.106 Soldier of Jah Army 0.0 SOVNZSZ12AB018A9B8 208.289 125.882 1.0 0.0 Rastaman 2003.0 -1.0
ARVVZQP11E2835DBCB 0.0 0.0 Wavves 133.25016 0.0 0.0 0.282 0.596 Wavvves 0.471578247701 SOJTQHQ12A8C143C5F 128.116 89.519 1.0 0.0 I Want To See You (And Go To The Movies) 2009.0 -1.0
ARFG9M11187FB3BBCB 0.0 0.0 Nashua USA C-Side 247.32689 0.0 9.0 0.612 -4.896 Santa Festival Compilation 2008 vol.1 0.0 SOAJSQL12AB0180501 242.196 171.278 5.0 1.0 Loose on the Dancefloor 0.0 225261.0
ARK4Z2O1187FB45FF0 0.0 0.0 Harvest 337.05751 0.247 4.0 0.46 -9.092 Underground Community 0.0 SOTDRVW12AB018BEB9 327.436 84.986 4.0 0.673 No Return 0.0 101619.0
AR4VQSG1187FB57E18 35.25082 -91.74015 Searcy, AR Gossip 430.23628 0.0 2.0 3.4e-2 -6.846 Yr Mangled Heart 0.0 SOTVOCL12A8AE478DD 424.06 121.998 4.0 0.847 Yr Mangled Heart 2006.0 740623.0
ARNBV1X1187B996249 0.0 0.0 Alex 186.80118 0.0 4.0 0.641 -16.108 Jolgaledin 0.0 SODTGRY12AB0182438 166.156 140.735 4.0 5.5e-2 Mariu Sonur Jesus 0.0 673970.0
ARXOEZX1187B9B82A1 0.0 0.0 Elie Attieh 361.89995 0.0 7.0 0.863 -4.919 ELITE 0.0 SOIINTJ12AB0180BA6 354.476 128.024 4.0 0.399 Fe Yom We Leila 0.0 280304.0
ARXPUIA1187B9A32F1 0.0 0.0 Rome, Italy Simone Cristicchi 220.00281 2.119 4.0 0.486 -6.52 Dall'Altra Parte Del Cancello 0.484225272411 SONHXJK12AAF3B5290 214.761 99.954 1.0 0.928 L'Italiano 2007.0 745962.0
ARNPPTH1187B9AD429 51.4855 -0.37196 Heston, Middlesex, England Jimmy Page 156.86485 0.334 7.0 0.493 -9.962 No Introduction Necessary [Deluxe Edition] 0.0 SOGUHGW12A58A80E06 149.269 162.48 4.0 0.534 Wailing Sounds 2004.0 599250.0
AROGWRA122988FEE45 0.0 0.0 Christos Dantis 256.67873 2.537 9.0 0.742 -13.404 Daktilika Apotipomata 0.0 SOJJOYI12A8C13399D 248.912 134.944 4.0 0.162 Stin Proigoumeni Zoi 0.0 611396.0

Next up is exploring this data. Click on the Exploration notebook to continue the tutorial.

ScaDaMaLe Course site and book

Million Song Dataset - Kaggle Challenge

Predict which songs a user will listen to.

SOURCE: This is just a Scala-rification of the Python notebook published in databricks community edition in 2016.

Stage 2: Exploring songs data

Explore

This is the second notebook in this tutorial. In this notebook we do what any data scientist does with their data right after parsing it: exploring and understanding different aspect of data. Make sure you understand how we get the songsTable by reading and running the ETL notebook. In the ETL notebook we created and cached a temporary table named songsTable

// Let's quickly do everything to register the tempView of the table here

// fill in comment ... EXERCISE!
case class Song(artist_id: String, artist_latitude: Double, artist_longitude: Double, artist_location: String, artist_name: String, duration: Double, end_of_fade_in: Double, key: Int, key_confidence: Double, loudness: Double, release: String, song_hotness: Double, song_id: String, start_of_fade_out: Double, tempo: Double, time_signature: Double, time_signature_confidence: Double, title: String, year: Double, partial_sequence: Int)

def parseLine(line: String): Song = {
  // fill in comment ...
  
  def toDouble(value: String, defaultVal: Double): Double = {
    try {
       value.toDouble
    } catch {
      case e: Exception => defaultVal
    }
  }

  def toInt(value: String, defaultVal: Int): Int = {
    try {
       value.toInt
      } catch {
      case e: Exception => defaultVal
    }
  }
  // fill in comment ...
  val tokens = line.split("\t")
  Song(tokens(0), toDouble(tokens(1), 0.0), toDouble(tokens(2), 0.0), tokens(3), tokens(4), toDouble(tokens(5), 0.0), toDouble(tokens(6), 0.0), toInt(tokens(7), -1), toDouble(tokens(8), 0.0), toDouble(tokens(9), 0.0), tokens(10), toDouble(tokens(11), 0.0), tokens(12), toDouble(tokens(13), 0.0), toDouble(tokens(14), 0.0), toDouble(tokens(15), 0.0), toDouble(tokens(16), 0.0), tokens(17), toDouble(tokens(18), 0.0), toInt(tokens(19), -1))
}

// this is loads all the data - a subset of the 1M songs dataset
val dataRDD = sc.textFile("/databricks-datasets/songs/data-001/part-*") 

// .. fill in comment
val df = dataRDD.map(parseLine).toDF

// .. fill in comment
df.createOrReplaceTempView("songsTable")
defined class Song
parseLine: (line: String)Song
dataRDD: org.apache.spark.rdd.RDD[String] = /databricks-datasets/songs/data-001/part-* MapPartitionsRDD[81] at textFile at command-2971213210276755:30
df: org.apache.spark.sql.DataFrame = [artist_id: string, artist_latitude: double ... 18 more fields]
spark.catalog.listTables.show(false) // make sure the temp view of our table is there
+----------------------------+--------+-----------+---------+-----------+
|name                        |database|description|tableType|isTemporary|
+----------------------------+--------+-----------+---------+-----------+
|countrycodes                |default |null       |EXTERNAL |false      |
|ltcar_locations_2_csv       |default |null       |MANAGED  |false      |
|magellan                    |default |null       |MANAGED  |false      |
|mobile_sample               |default |null       |EXTERNAL |false      |
|over300all_2_txt            |default |null       |MANAGED  |false      |
|person                      |default |null       |MANAGED  |false      |
|persons                     |default |null       |MANAGED  |false      |
|social_media_usage          |default |null       |MANAGED  |false      |
|social_media_usage_csv_gui  |default |null       |MANAGED  |false      |
|voronoi20191213uppsla1st_txt|default |null       |MANAGED  |false      |
|voronoi20191213uppsla2d_txt |default |null       |MANAGED  |false      |
|voronoi20191213uppsla3d_txt |default |null       |MANAGED  |false      |
|songstable                  |null    |null       |TEMPORARY|true       |
+----------------------------+--------+-----------+---------+-----------+

A first inspection

A first step to any data exploration is viewing sample data. For this purpose we can use a simple SQL query that returns first 10 rows.

select * from songsTable limit 10
artist_id artist_latitude artist_longitude artist_location artist_name duration end_of_fade_in key key_confidence loudness release song_hotness song_id start_of_fade_out tempo time_signature time_signature_confidence title year partial_sequence
AR81V6H1187FB48872 0.0 0.0 Earl Sixteen 213.7073 0.0 11.0 0.419 -12.106 Soldier of Jah Army 0.0 SOVNZSZ12AB018A9B8 208.289 125.882 1.0 0.0 Rastaman 2003.0 -1.0
ARVVZQP11E2835DBCB 0.0 0.0 Wavves 133.25016 0.0 0.0 0.282 0.596 Wavvves 0.471578247701 SOJTQHQ12A8C143C5F 128.116 89.519 1.0 0.0 I Want To See You (And Go To The Movies) 2009.0 -1.0
ARFG9M11187FB3BBCB 0.0 0.0 Nashua USA C-Side 247.32689 0.0 9.0 0.612 -4.896 Santa Festival Compilation 2008 vol.1 0.0 SOAJSQL12AB0180501 242.196 171.278 5.0 1.0 Loose on the Dancefloor 0.0 225261.0
ARK4Z2O1187FB45FF0 0.0 0.0 Harvest 337.05751 0.247 4.0 0.46 -9.092 Underground Community 0.0 SOTDRVW12AB018BEB9 327.436 84.986 4.0 0.673 No Return 0.0 101619.0
AR4VQSG1187FB57E18 35.25082 -91.74015 Searcy, AR Gossip 430.23628 0.0 2.0 3.4e-2 -6.846 Yr Mangled Heart 0.0 SOTVOCL12A8AE478DD 424.06 121.998 4.0 0.847 Yr Mangled Heart 2006.0 740623.0
ARNBV1X1187B996249 0.0 0.0 Alex 186.80118 0.0 4.0 0.641 -16.108 Jolgaledin 0.0 SODTGRY12AB0182438 166.156 140.735 4.0 5.5e-2 Mariu Sonur Jesus 0.0 673970.0
ARXOEZX1187B9B82A1 0.0 0.0 Elie Attieh 361.89995 0.0 7.0 0.863 -4.919 ELITE 0.0 SOIINTJ12AB0180BA6 354.476 128.024 4.0 0.399 Fe Yom We Leila 0.0 280304.0
ARXPUIA1187B9A32F1 0.0 0.0 Rome, Italy Simone Cristicchi 220.00281 2.119 4.0 0.486 -6.52 Dall'Altra Parte Del Cancello 0.484225272411 SONHXJK12AAF3B5290 214.761 99.954 1.0 0.928 L'Italiano 2007.0 745962.0
ARNPPTH1187B9AD429 51.4855 -0.37196 Heston, Middlesex, England Jimmy Page 156.86485 0.334 7.0 0.493 -9.962 No Introduction Necessary [Deluxe Edition] 0.0 SOGUHGW12A58A80E06 149.269 162.48 4.0 0.534 Wailing Sounds 2004.0 599250.0
AROGWRA122988FEE45 0.0 0.0 Christos Dantis 256.67873 2.537 9.0 0.742 -13.404 Daktilika Apotipomata 0.0 SOJJOYI12A8C13399D 248.912 134.944 4.0 0.162 Stin Proigoumeni Zoi 0.0 611396.0
table("songsTable").printSchema()
root
 |-- artist_id: string (nullable = true)
 |-- artist_latitude: double (nullable = false)
 |-- artist_longitude: double (nullable = false)
 |-- artist_location: string (nullable = true)
 |-- artist_name: string (nullable = true)
 |-- duration: double (nullable = false)
 |-- end_of_fade_in: double (nullable = false)
 |-- key: integer (nullable = false)
 |-- key_confidence: double (nullable = false)
 |-- loudness: double (nullable = false)
 |-- release: string (nullable = true)
 |-- song_hotness: double (nullable = false)
 |-- song_id: string (nullable = true)
 |-- start_of_fade_out: double (nullable = false)
 |-- tempo: double (nullable = false)
 |-- time_signature: double (nullable = false)
 |-- time_signature_confidence: double (nullable = false)
 |-- title: string (nullable = true)
 |-- year: double (nullable = false)
 |-- partial_sequence: integer (nullable = false)
select count(*) from songsTable
count(1)
31369.0
table("songsTable").count() // or equivalently with DataFrame API - recall table("songsTable") is a DataFrame
res4: Long = 31369
display(sqlContext.sql("SELECT duration, year FROM songsTable")) // Aggregation is set to 'Average' in 'Plot Options'
duration year
213.7073 2003.0
133.25016 2009.0
247.32689 0.0
337.05751 0.0
430.23628 2006.0
186.80118 0.0
361.89995 0.0
220.00281 2007.0
156.86485 2004.0
256.67873 0.0
204.64281 0.0
112.48281 0.0
170.39628 0.0
215.95383 0.0
303.62077 0.0
266.60526 0.0
326.19057 1997.0
51.04281 2009.0
129.4624 0.0
253.33506 2003.0
237.76608 2004.0
132.96281 0.0
399.35955 2006.0
168.75057 1991.0
396.042 0.0
192.10404 1968.0
12.2771 2006.0
367.56853 0.0
189.93587 0.0
233.50812 0.0
462.68036 0.0
202.60526 0.0
241.52771 0.0
275.64363 1992.0
350.69342 2007.0
166.55628 1968.0
249.49506 1983.0
53.86404 1992.0
233.76934 2001.0
275.12118 2009.0
191.13751 2006.0
299.07546 0.0
468.74077 0.0
110.34077 0.0
234.78812 2003.0
705.25342 2006.0
383.52934 0.0
196.10077 0.0
299.20608 1998.0
94.04036 0.0
28.08118 2006.0
207.93424 2006.0
152.0322 1999.0
207.96036 2002.0
371.25179 0.0
288.93995 2002.0
235.93751 2004.0
505.70404 0.0
177.57995 0.0
376.842 2004.0
266.84036 2004.0
270.8371 2006.0
178.18077 0.0
527.17669 0.0
244.27057 0.0
436.47955 2006.0
236.79955 0.0
134.53016 2005.0
181.002 0.0
239.41179 1999.0
72.98567 0.0
214.36036 2001.0
150.59546 2007.0
152.45016 1970.0
218.17424 0.0
290.63791 0.0
149.05424 0.0
440.21506 0.0
212.34893 1988.0
278.67383 0.0
269.60934 1974.0
182.69995 2002.0
207.882 2007.0
102.50404 0.0
437.60281 0.0
216.11057 2009.0
193.25342 0.0
234.16118 2009.0
695.77098 0.0
297.58649 1996.0
265.37751 2000.0
182.85669 1990.0
202.23955 0.0
390.08608 2009.0
242.78159 2000.0
242.54649 2002.0
496.66567 2004.0
395.36281 0.0
234.89261 1999.0
237.84444 2005.0
313.57342 2009.0
489.22077 2001.0
239.98649 2004.0
128.65261 0.0
193.07057 0.0
144.19546 0.0
196.96281 2006.0
222.06649 1997.0
58.38322 0.0
346.14812 1998.0
406.54322 0.0
304.09098 2009.0
180.21832 2003.0
213.41995 0.0
323.44771 0.0
54.7522 2009.0
437.02812 1994.0
268.7473 2009.0
104.75057 0.0
248.60689 2006.0
221.41342 0.0
237.81832 1991.0
216.34567 2009.0
78.94159 0.0
47.22893 2005.0
202.00444 2007.0
293.56363 0.0
206.44526 1986.0
267.78077 2003.0
187.27138 2008.0
249.05098 2009.0
221.51791 0.0
452.88444 0.0
163.76118 1992.0
257.17506 0.0
235.78077 0.0
257.82812 1996.0
195.34322 0.0
478.1971 0.0
268.01587 1997.0
136.93342 1983.0
397.53098 0.0
194.69016 2001.0
580.80608 0.0
177.71057 2006.0
257.43628 1999.0
184.13669 0.0
64.57424 2001.0
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Exercises

  1. Why do you think average song durations increase dramatically in 70's?
  2. Add error bars with standard deviation around each average point in the plot.
  3. How did average loudness change over time?
  4. How did tempo change over time?
  5. What other aspects of songs can you explore with this technique?

Sampling and visualizing

You can dive deep into Scala visualisations here: - https://docs.databricks.com/notebooks/visualizations/charts-and-graphs-scala.html

You can also use R and Python for visualisations in the same notebook: - https://docs.databricks.com/notebooks/visualizations/index.html

ScaDaMaLe Course site and book

Million Song Dataset - Kaggle Challenge

Predict which songs a user will listen to.

SOURCE: This is just a Scala-rification of the Python notebook published in databricks community edition in 2016.

Stage 3: Modeling Songs via k-means

Model

This is the third step into our project. In the first step we parsed raw text files and created a table. Then we explored different aspects of data and learned that things have been changing over time. In this step we attempt to gain deeper understanding of our data by categorizing (a.k.a. clustering) our data. For the sake of training we pick a fairly simple model based on only three parameters. We leave more sophisticated modeling as exercies to the reader

We pick the most commonly used and simplest clustering algorithm (KMeans) for our job. The SparkML KMeans implementation expects input in a vector column. Fortunately, there are already utilities in SparkML that can help us convert existing columns in our table to a vector field. It is called VectorAssembler. Here we import that functionality and use it to create a new DataFrame

// Let's quickly do everything to register the tempView of the table here

// this is a case class for our row objects
case class Song(artist_id: String, artist_latitude: Double, artist_longitude: Double, artist_location: String, artist_name: String, duration: Double, end_of_fade_in: Double, key: Int, key_confidence: Double, loudness: Double, release: String, song_hotness: Double, song_id: String, start_of_fade_out: Double, tempo: Double, time_signature: Double, time_signature_confidence: Double, title: String, year: Double, partial_sequence: Int)

def parseLine(line: String): Song = {
  // this is robust parsing by try-catching type exceptions
  
  def toDouble(value: String, defaultVal: Double): Double = {
    try {
       value.toDouble
    } catch {
      case e: Exception => defaultVal
    }
  }

  def toInt(value: String, defaultVal: Int): Int = {
    try {
       value.toInt
      } catch {
      case e: Exception => defaultVal
    }
  }
  // splitting the sting of each line by the delimiter TAB character '\t'
  val tokens = line.split("\t")
  
  // making song objects
  Song(tokens(0), toDouble(tokens(1), 0.0), toDouble(tokens(2), 0.0), tokens(3), tokens(4), toDouble(tokens(5), 0.0), toDouble(tokens(6), 0.0), toInt(tokens(7), -1), toDouble(tokens(8), 0.0), toDouble(tokens(9), 0.0), tokens(10), toDouble(tokens(11), 0.0), tokens(12), toDouble(tokens(13), 0.0), toDouble(tokens(14), 0.0), toDouble(tokens(15), 0.0), toDouble(tokens(16), 0.0), tokens(17), toDouble(tokens(18), 0.0), toInt(tokens(19), -1))
}

// this is loads all the data - a subset of the 1M songs dataset
val dataRDD = sc.textFile("/databricks-datasets/songs/data-001/part-*") 

// .. fill in comment
val df = dataRDD.map(parseLine).toDF

// .. fill in comment
df.createOrReplaceTempView("songsTable")
defined class Song
parseLine: (line: String)Song
dataRDD: org.apache.spark.rdd.RDD[String] = /databricks-datasets/songs/data-001/part-* MapPartitionsRDD[106] at textFile at command-2971213210277067:32
df: org.apache.spark.sql.DataFrame = [artist_id: string, artist_latitude: double ... 18 more fields]
import org.apache.spark.ml.feature.VectorAssembler

val trainingData = new VectorAssembler()
                      .setInputCols(Array("duration", "tempo", "loudness"))
                      .setOutputCol("features")
                      .transform(table("songsTable"))
import org.apache.spark.ml.feature.VectorAssembler
trainingData: org.apache.spark.sql.DataFrame = [artist_id: string, artist_latitude: double ... 19 more fields]

All we have done above with the VectorAssembler method is:

  • created a DataFrame called trainingData
  • that transformed our table called songsTable
  • by adding an output column named features using setOutputCol("features")
  • that was obtained from an Array of the songsTable's columns named duration, tempo and loudness using
    • setInputCols(Array("duration", "tempo", "loudness")).
trainingData.take(3) // see first 3 rows of trainingData DataFrame, notice the vectors in the last column
res3: Array[org.apache.spark.sql.Row] = Array([AR81V6H1187FB48872,0.0,0.0,,Earl Sixteen,213.7073,0.0,11,0.419,-12.106,Soldier of Jah Army,0.0,SOVNZSZ12AB018A9B8,208.289,125.882,1.0,0.0,Rastaman,2003.0,-1,[213.7073,125.882,-12.106]], [ARVVZQP11E2835DBCB,0.0,0.0,,Wavves,133.25016,0.0,0,0.282,0.596,Wavvves,0.471578247701,SOJTQHQ12A8C143C5F,128.116,89.519,1.0,0.0,I Want To See You (And Go To The Movies),2009.0,-1,[133.25016,89.519,0.596]], [ARFG9M11187FB3BBCB,0.0,0.0,Nashua USA,C-Side,247.32689,0.0,9,0.612,-4.896,Santa Festival Compilation 2008 vol.1,0.0,SOAJSQL12AB0180501,242.196,171.278,5.0,1.0,Loose on the Dancefloor,0.0,225261,[247.32689,171.278,-4.896]])

Transformers

A Transformer is an abstraction that includes feature transformers and learned models. Technically, a Transformer implements a method transform(), which converts one DataFrame into another, generally by appending one or more columns. For example:

  • A feature transformer might take a DataFrame, read a column (e.g., text), map it into a new column (e.g., feature vectors), and output a new DataFrame with the mapped column appended.
  • A learning model might take a DataFrame, read the column containing feature vectors, predict the label for each feature vector, and output a new DataFrame with predicted labels appended as a column.

Estimators

An Estimator abstracts the concept of a learning algorithm or any algorithm that fits or trains on data.

Technically, an Estimator implements a method fit(), which accepts a DataFrame and produces a Model, which is a Transformer.

For example, a learning algorithm such as LogisticRegression is an Estimator, and calling fit() trains a LogisticRegressionModel, which is a Model and hence a Transformer.

display(trainingData.select("duration", "tempo", "loudness", "features").limit(5)) // see features in more detail

Demonstration of the standard algorithm

(1) (2) (3) (4)

  1. k initial "means" (in this case k=3) are randomly generated within the data domain (shown in color).
  • k clusters are created by associating every observation with the nearest mean. The partitions here represent the Voronoi diagram generated by the means.
  • The centroid of each of the k clusters becomes the new mean.
  • Steps 2 and 3 are repeated until local convergence has been reached.

The "assignment" step 2 is also referred to as expectation step, the "update step" 3 as maximization step, making this algorithm a variant of the generalized expectation-maximization algorithm.

Caveats: As k-means is a heuristic algorithm, there is no guarantee that it will converge to the global optimum, and the result may depend on the initial clusters. As the algorithm is usually very fast, it is common to run it multiple times with different starting conditions. However, in the worst case, k-means can be very slow to converge. For more details see https://en.wikipedia.org/wiki/K-means_clustering that is also embedded in-place below.

CAUTION!

Iris flower data set, clustered using

  • k-means (left) and
  • true species in the data set (right).

k-means clustering result for the Iris flower data set and actual species visualized using ELKI. Cluster means are marked using larger, semi-transparent symbols.

Note that k-means is non-determinicstic, so results vary. Cluster means are visualized using larger, semi-transparent markers. The visualization was generated using ELKI.

With some cautionary tales we go ahead with applying k-means to our dataset next.

We can now pass this new DataFrame to the KMeans model and ask it to categorize different rows in our data to two different classes (setK(2)). We place the model in a immutable value named model.

Note: This command performs multiple spark jobs (one job per iteration in the KMeans algorithm). You will see the progress bar starting over and over again.

import org.apache.spark.ml.clustering.KMeans
val model = new KMeans().setK(2).fit(trainingData) // 37 seconds in 5 workers cluster
import org.apache.spark.ml.clustering.KMeans
model: org.apache.spark.ml.clustering.KMeansModel = KMeansModel: uid=kmeans_a1617b1902bd, k=2, distanceMeasure=euclidean, numFeatures=3
//model. // uncomment and place cursor next to . and hit Tab to see all methods on model
model.clusterCenters // get cluster centres
res5: Array[org.apache.spark.ml.linalg.Vector] = Array([208.72069181761955,124.38376303683947,-9.986137113920133], [441.1413218945455,123.00973381818183,-10.560375818181816])
val modelTransformed = model.transform(trainingData) // to get predictions as last column
modelTransformed: org.apache.spark.sql.DataFrame = [artist_id: string, artist_latitude: double ... 20 more fields]

Remember that ML Pipelines works with DataFrames. So, our trainingData and modelTransformed are both DataFrames

trainingData.printSchema
root
 |-- artist_id: string (nullable = true)
 |-- artist_latitude: double (nullable = false)
 |-- artist_longitude: double (nullable = false)
 |-- artist_location: string (nullable = true)
 |-- artist_name: string (nullable = true)
 |-- duration: double (nullable = false)
 |-- end_of_fade_in: double (nullable = false)
 |-- key: integer (nullable = false)
 |-- key_confidence: double (nullable = false)
 |-- loudness: double (nullable = false)
 |-- release: string (nullable = true)
 |-- song_hotness: double (nullable = false)
 |-- song_id: string (nullable = true)
 |-- start_of_fade_out: double (nullable = false)
 |-- tempo: double (nullable = false)
 |-- time_signature: double (nullable = false)
 |-- time_signature_confidence: double (nullable = false)
 |-- title: string (nullable = true)
 |-- year: double (nullable = false)
 |-- partial_sequence: integer (nullable = false)
 |-- features: vector (nullable = true)
modelTransformed.printSchema
root
 |-- artist_id: string (nullable = true)
 |-- artist_latitude: double (nullable = false)
 |-- artist_longitude: double (nullable = false)
 |-- artist_location: string (nullable = true)
 |-- artist_name: string (nullable = true)
 |-- duration: double (nullable = false)
 |-- end_of_fade_in: double (nullable = false)
 |-- key: integer (nullable = false)
 |-- key_confidence: double (nullable = false)
 |-- loudness: double (nullable = false)
 |-- release: string (nullable = true)
 |-- song_hotness: double (nullable = false)
 |-- song_id: string (nullable = true)
 |-- start_of_fade_out: double (nullable = false)
 |-- tempo: double (nullable = false)
 |-- time_signature: double (nullable = false)
 |-- time_signature_confidence: double (nullable = false)
 |-- title: string (nullable = true)
 |-- year: double (nullable = false)
 |-- partial_sequence: integer (nullable = false)
 |-- features: vector (nullable = true)
 |-- prediction: integer (nullable = false)
  • The column features that we specified as output column to our VectorAssembler contains the features
  • The new column prediction in modelTransformed contains the predicted output
val transformed = modelTransformed.select("duration", "tempo", "loudness", "prediction")
transformed: org.apache.spark.sql.DataFrame = [duration: double, tempo: double ... 2 more fields]

To comfortably visualize the data we produce a random sample. Remember the display() function? We can use it to produce a nicely rendered table of transformed DataFrame.

// just sampling the fraction 0.005 of all the rows at random, 
// 'false' argument to sample is for sampling without replacement
display(transformed.sample(false, fraction = 0.005, 12988934L)) 
duration tempo loudness prediction
265.97832 129.987 -5.065 0.0
306.36363 127.529 -8.273 0.0
195.73506 115.191 -6.327 0.0
257.82812 92.892 -13.621 0.0
177.55383 149.853 -10.969 0.0
224.9922 97.98 -5.921 0.0
528.09098 160.022 -5.956 1.0
213.68118 100.219 -4.528 0.0
35.52608 121.349 -18.721 0.0
213.68118 120.581 -10.633 0.0
300.53832 139.017 -13.319 0.0
138.81424 160.044 -11.138 0.0
413.962 89.588 -13.143 1.0
292.17914 188.543 -5.389 0.0
419.34322 140.008 -5.389 1.0
261.61587 152.951 -12.447 0.0
168.64608 99.617 -8.164 0.0
446.27546 196.005 -6.621 1.0
343.92771 122.877 -10.264 1.0
261.69424 145.129 -4.733 0.0
408.47628 61.259 -11.244 1.0
243.3824 161.778 -6.88 0.0
184.00608 111.461 -9.788 0.0
67.39546 188.723 -3.239 0.0
165.51138 81.125 -18.692 0.0
214.85669 144.174 -17.989 0.0
185.96526 186.897 -6.041 0.0
170.05669 75.356 -16.486 0.0
193.72363 117.131 -9.822 0.0
227.23873 91.953 -11.221 0.0
177.6322 150.962 -7.288 0.0
117.21098 100.021 -10.782 0.0
422.42567 91.214 -8.872 1.0
145.162 95.388 -10.166 0.0
242.93832 112.015 -7.135 0.0
366.00118 65.05 -13.768 1.0
601.15546 70.623 -11.179 1.0
196.17914 121.563 -5.434 0.0
399.35955 124.963 -3.415 1.0
287.73832 161.648 -14.721 0.0
285.09995 132.86 -10.23 0.0
358.32118 132.874 -6.071 1.0
407.71873 85.996 -10.103 1.0
463.25506 95.083 -6.4 1.0
295.91465 93.515 -8.987 0.0
273.8673 190.044 -10.556 0.0
280.73751 113.363 -6.893 0.0
142.65424 206.067 -7.996 0.0
197.38077 84.023 -10.964 0.0
226.24608 166.768 -5.941 0.0
152.47628 153.528 -7.393 0.0
315.32363 139.919 -7.438 0.0
329.03791 180.059 -6.473 1.0
296.88118 137.976 -5.49 0.0
250.77506 84.543 -18.058 0.0
48.14322 52.814 -11.617 0.0
290.16771 141.24 -14.009 0.0
406.04689 133.997 -9.685 1.0
124.57751 161.237 -12.314 0.0
280.45016 154.003 -8.094 0.0
472.31955 219.371 -6.08 1.0
267.4673 152.123 -18.457 0.0
216.21506 88.022 -7.096 0.0
31.00689 237.737 -11.538 0.0
283.21914 132.934 -11.153 0.0
284.21179 110.585 -15.384 0.0
154.87955 157.881 -4.377 0.0
431.46404 113.905 -8.651 1.0
215.87546 124.572 -7.67 0.0
161.43628 43.884 -14.936 0.0
29.09995 135.146 -1.837 0.0
301.68771 123.672 -9.293 0.0
170.10893 124.022 -9.589 0.0
281.96526 63.544 -8.25 0.0
484.54485 149.565 -5.501 1.0
135.1571 92.749 -7.881 0.0
180.45342 137.899 -5.246 0.0
142.44526 85.406 -11.305 0.0
209.3971 93.233 -13.079 0.0
319.9473 122.936 -5.98 0.0
55.82322 249.325 -8.656 0.0
192.88771 124.006 -5.745 0.0
624.14322 128.988 -7.872 1.0
188.49914 107.264 -13.24 0.0
148.32281 150.075 -5.793 0.0
195.00363 49.31 -14.54 0.0
130.61179 100.208 -10.487 0.0
212.11383 111.048 -4.749 0.0
204.56444 92.076 -7.906 0.0
292.04853 135.932 -9.004 0.0
377.83465 73.336 -13.457 1.0
246.96118 116.761 -8.117 0.0
90.30485 39.3 -15.444 0.0
201.92608 123.558 -9.857 0.0
282.06975 136.09 -6.202 0.0
194.55955 119.488 -16.454 0.0
318.4322 140.467 -6.375 0.0
55.45751 121.476 -7.891 0.0
275.30404 90.024 -6.191 0.0
422.24281 131.994 -8.786 1.0
269.47873 88.921 -4.419 0.0
186.01751 55.271 -16.153 0.0
221.17832 94.967 -6.591 0.0
275.66975 94.999 -16.843 0.0
335.28118 90.129 -13.33 1.0
288.88771 102.96 -10.967 0.0
190.71955 88.269 -13.167 0.0
211.17342 126.741 -10.398 0.0
116.92363 140.09 -7.578 0.0
310.282 181.753 -17.61 0.0
184.21506 112.336 -8.764 0.0
248.21506 101.988 -6.487 0.0
116.00934 84.793 -9.057 0.0
299.88526 143.66 -7.279 0.0
1376.78322 107.066 -7.893 1.0
182.85669 191.559 -10.367 0.0
238.2624 48.592 -9.687 0.0
239.5424 105.47 -9.258 0.0
195.16036 127.911 -7.054 0.0
149.73342 118.643 -10.526 0.0
424.30649 62.8 -22.35 1.0
221.77914 104.983 -7.908 0.0
407.7971 126.983 -11.675 1.0
175.04608 120.542 -17.484 0.0
306.65098 120.0 -18.973 0.0
315.0624 85.82 -11.858 0.0
88.5024 211.429 -11.543 0.0
101.61587 19.215 -26.402 0.0
132.04853 186.123 -7.21 0.0
146.25914 200.16 -15.88 0.0
147.3824 104.658 -8.836 0.0
156.26404 135.353 -8.245 0.0
66.2722 115.129 -16.416 0.0
247.43138 124.991 -11.79 0.0
282.90567 115.472 -12.448 0.0
401.05751 125.015 -9.465 1.0
156.08118 88.128 -16.916 0.0
198.08608 133.961 -8.055 0.0
214.09914 84.353 -12.991 0.0
269.73995 161.953 -3.091 0.0
199.44444 169.922 -6.241 0.0
149.65506 190.802 -30.719 0.0
227.23873 120.14 -12.39 0.0

To generate a scatter plot matrix, click on the plot button bellow the table and select scatter. That will transform your table to a scatter plot matrix. It automatically picks all numeric columns as values. To include predicted clusters, click on Plot Options and drag prediction to the list of Keys. You will get the following plot. On the diagonal panels you see the PDF of marginal distribution of each variable. Non-diagonal panels show a scatter plot between variables of the two variables of the row and column. For example the top right panel shows the scatter plot between duration and loudness. Each point is colored according to the cluster it is assigned to.

display(transformed.sample(false, fraction = 0.01)) // try fraction=1.0 as this dataset is small
duration tempo loudness prediction
189.93587 134.957 -12.934 0.0
206.44526 135.26 -11.146 0.0
295.65342 137.904 -7.308 0.0
158.1971 174.831 -12.544 0.0
259.99628 171.094 -12.057 0.0
277.002 88.145 -6.039 0.0
1518.65424 65.003 -19.182 1.0
121.73016 85.041 -8.193 0.0
205.97506 106.952 -6.572 0.0
206.18404 89.447 -9.535 0.0
202.52689 134.13 -6.535 0.0
259.02975 97.948 -11.276 0.0
308.53179 80.017 -12.277 0.0
151.71873 117.179 -12.394 0.0
165.56363 99.187 -11.414 0.0
370.83383 67.495 -20.449 1.0
238.65424 100.071 -9.276 0.0
163.7873 119.924 -5.941 0.0
279.32689 67.371 -26.67 0.0
353.85424 68.405 -8.105 1.0
227.23873 117.62 -7.874 0.0
195.49995 85.916 -8.828 0.0
322.45506 135.826 -5.034 0.0
235.88526 109.773 -10.919 0.0
235.15383 163.924 -9.666 0.0
253.67465 125.014 -7.171 0.0
415.03302 71.991 -15.224 1.0
190.85016 152.805 -2.871 0.0
290.76853 84.841 -6.161 0.0
346.8273 129.981 -10.377 1.0
174.70649 143.446 -11.994 0.0
170.84036 70.033 -7.782 0.0
517.66812 151.948 -12.363 1.0
62.06649 154.406 -9.387 0.0
505.96526 90.59 -19.848 1.0
480.86159 0.0 -11.707 1.0
330.13506 204.534 -9.85 1.0
223.99955 110.3 -12.339 0.0
200.98567 89.215 -3.858 0.0
158.09261 178.826 -13.681 0.0
186.46159 110.102 -16.477 0.0
399.46404 125.03 -10.786 1.0
118.64771 85.747 -34.461 0.0
352.49587 91.139 -9.13 1.0
150.15138 106.364 -7.337 0.0
158.98077 124.54 -17.405 0.0
122.17424 170.018 -9.047 0.0
299.38893 91.976 -6.266 0.0
197.95546 142.744 -8.189 0.0
332.38159 89.071 -5.08 1.0
309.78567 136.05 -15.105 0.0
198.47791 82.546 -12.594 0.0
254.17098 144.01 -9.0 0.0
155.81995 233.022 -8.978 0.0
176.53506 136.255 -9.675 0.0
331.54567 221.511 -13.778 1.0
140.72118 162.44 -10.654 0.0
210.9122 120.039 -5.391 0.0
197.27628 119.396 -22.599 0.0
339.25179 96.842 -16.207 1.0
355.97016 142.777 -5.118 1.0
170.23955 55.107 -17.654 0.0
360.01914 119.997 -7.53 1.0
241.76281 101.938 -3.765 0.0
84.92363 236.863 -15.846 0.0
361.09016 120.121 -5.861 1.0
262.37342 89.924 -4.819 0.0
225.74975 139.994 -11.505 0.0
246.9873 172.147 -16.273 0.0
159.242 166.855 -4.771 0.0
192.86159 148.297 -13.423 0.0
140.90404 92.602 -12.604 0.0
224.20853 71.879 -16.615 0.0
235.78077 180.366 -3.918 0.0
244.45342 105.077 -5.004 0.0
210.57261 200.044 -11.381 0.0
327.3922 112.023 -11.341 1.0
168.38485 99.991 -4.1 0.0
287.13751 137.154 -12.948 0.0
148.63628 121.773 -11.432 0.0
214.7522 124.437 -5.834 0.0
197.43302 92.959 -4.948 0.0
150.17751 112.0 -5.968 0.0
152.86812 120.884 -15.693 0.0
173.322 120.827 -7.96 0.0
235.15383 85.519 -8.172 0.0
299.41506 94.68 -15.486 0.0
222.35383 156.046 -8.885 0.0
235.85914 130.055 -5.341 0.0
276.71465 170.059 -2.926 0.0
136.07138 168.895 -6.971 0.0
205.7922 129.57 -6.113 0.0
268.72118 126.894 -7.142 0.0
390.63465 232.08 -5.493 1.0
242.59873 124.034 -11.24 0.0
274.80771 108.178 -21.456 0.0
157.25669 151.108 -11.678 0.0
203.67628 140.02 -5.939 0.0
302.47138 148.2 -10.428 0.0
292.64934 106.006 -3.538 0.0
245.002 135.997 -10.6 0.0
181.57669 132.89 -5.429 0.0
36.38812 65.132 -12.621 0.0
656.14322 95.469 -8.588 1.0
262.50404 88.025 -4.359 0.0
261.95546 117.93 -5.5 0.0
337.57995 122.08 -6.658 1.0
373.08036 126.846 -10.115 1.0
220.36853 157.934 -13.192 0.0
357.22404 199.889 -9.832 1.0
663.61424 143.681 -9.066 1.0
155.08853 201.152 -7.43 0.0
264.56771 133.7 -11.767 0.0
262.53016 105.041 -3.933 0.0
386.61179 132.644 -8.34 1.0
224.41751 93.333 -12.001 0.0
264.25424 117.547 -6.134 0.0
12.82567 99.229 -29.527 0.0
470.25587 135.99 -7.403 1.0
213.7073 92.584 -8.398 0.0
50.59873 108.989 -10.006 0.0
273.162 114.014 -8.527 0.0
285.1522 101.877 -9.361 0.0
267.88526 123.903 -10.177 0.0
334.54975 138.386 -7.389 1.0
174.0273 95.084 -21.944 0.0
242.15465 87.196 -9.749 0.0
188.96934 188.967 -3.288 0.0
480.67873 127.989 -7.243 1.0
182.54322 72.894 -17.837 0.0
231.1571 126.959 -5.632 0.0
105.37751 136.156 -13.607 0.0
125.88363 93.022 -13.496 0.0
216.99873 151.866 -7.47 0.0
176.50893 142.601 -3.881 0.0
245.57669 123.186 -3.609 0.0
191.37261 145.008 -14.3 0.0
62.11873 80.961 -12.453 0.0
274.80771 83.505 -10.032 0.0
148.29669 92.154 -13.542 0.0
241.47546 115.886 -11.948 0.0
250.40934 100.001 -18.335 0.0
154.56608 96.464 -12.133 0.0
485.14567 84.633 -8.812 1.0
307.22567 63.498 -9.047 0.0
167.78404 122.92 -13.528 0.0
345.10322 130.003 -7.858 1.0
178.9122 111.13 -7.33 0.0
237.29587 111.244 -15.209 0.0
230.16444 74.335 -12.244 0.0
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displayHTML(frameIt("https://en.wikipedia.org/wiki/Euclidean_space",500)) // make sure you run the cell with first wikipedia article!

Do you see the problem in our clusters based on the plot?

As you can see there is very little "separation" (in the sense of being separable into two point clouds, that represent our two identifed clusters, such that they have minimal overlay of these two features, i.e. tempo and loudness. NOTE that this sense of "pairwise separation" is a 2D projection of all three features in 3D Euclidean Space, i.e. loudness, tempo and duration, that depends directly on their two-dimensional visually sense-making projection of perhaps two important song features, as depicted in the corresponding 2D-scatter-plot of tempo versus loudness within the 2D scatter plot matrix that is helping us to partially visualize in the 2D-plane all of the three features in the three dimensional real-valued feature space that was the input to our K-Means algorithm) between loudness, and tempo and generated clusters. To see that, focus on the panels in the first and second columns of the scatter plot matrix. For varying values of loudness and tempo prediction does not change. Instead, duration of a song alone predicts what cluster it belongs to. Why is that?

To see the reason, let's take a look at the marginal distribution of duration in the next cell.

To produce this plot, we have picked histogram from the plots menu and in Plot Options we chose prediction as key and duration as value. The histogram plot shows significant skew in duration. Basically there are a few very long songs. These data points have large leverage on the mean function (what KMeans uses for clustering).

display(transformed.sample(false, fraction = 1.0).select("duration", "prediction")) // plotting over all results
duration prediction
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There are known techniques for dealing with skewed features. A simple technique is applying a power transformation. We are going to use the simplest and most common power transformation: logarithm.

In following cell we repeat the clustering experiment with a transformed DataFrame that includes a new column called log_duration.

val df = table("songsTable").selectExpr("tempo", "loudness", "log(duration) as log_duration")
val trainingData2 = new VectorAssembler().
                  setInputCols(Array("log_duration", "tempo", "loudness")).
                  setOutputCol("features").
                  transform(df)
val model2 = new KMeans().setK(2).fit(trainingData2)
val transformed2 = model2.transform(trainingData2).select("log_duration", "tempo", "loudness", "prediction")
display(transformed2.sample(false, fraction = 0.1))
log_duration tempo loudness prediction
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5.101912321360921 144.581 -10.228 0.0
5.607287873701992 94.022 -11.182 1.0
5.464231047351683 80.56 -5.019 1.0
5.82628048105143 144.995 -7.894 0.0
5.11862145971635 95.003 -6.393 1.0
5.226542700885508 144.35 -5.396 0.0
5.764803190566032 112.0 -9.303 1.0
4.7352630988107265 114.697 -4.575 1.0
5.316018719084458 141.976 -21.61 0.0
5.733516795474041 183.021 -11.119 0.0
5.305829678341554 86.122 -4.442 1.0
5.934733177365839 124.97 -18.222 1.0
5.253812766217677 96.969 -3.996 1.0
5.411294114932506 89.874 -6.8 1.0
4.551471791137433 80.11 -12.882 1.0
5.24654895931225 126.857 -11.178 1.0
5.52538935145276 88.999 -7.108 1.0
5.233395411909235 174.002 -4.727 0.0
5.062519840326649 172.201 -4.75 0.0
5.47709335356482 130.832 -19.444 1.0
6.546896021572621 175.921 -14.61 0.0
5.875580463550244 125.238 -8.638 1.0
5.547621681459602 182.05 -8.294 0.0
5.600552539550706 165.987 -5.869 0.0
5.330541303481353 100.578 -13.527 1.0
5.521426437267798 98.619 -8.239 1.0
5.0512127147107515 100.524 -13.862 1.0

The new clustering model makes much more sense. Songs with high tempo and loudness are put in one cluster and song duration does not affect song categories.

To really understand how the points in 3D behave you need to see them in 3D interactively and understand the limits of its three 2D projections. For this let us spend some time and play in sageMath Worksheet in CoCalc (it is free for light-weight use and perhaps worth the 7 USD a month if you need more serious computing in mathmeatics, statistics, etc. in multiple languages!).

Let us take a look at this sageMath Worksheet published here:

The point of the above little example is that you need to be able to tell a sensible story with your data science process and not just blindly apply a heuristic, but highly scalable, algorithm which depends on the notion of nearest neighborhoods defined by the metric (Euclidean distances in 3-dimensional real-valued spaces in this example) induced by the features you have engineered or have the power to re/re/...-engineer to increase the meaningfullness of the problem at hand.

Determining Optimal K

There are methods to find the optimal number of clusters. This partly depends on the purpose of the unsupervised learning task.

See here for some metrics in scala for the Irish dataset.

ScaDaMaLe Course site and book

Supervised Clustering with Decision Trees

Visual Introduction to decision trees and application to hand-written digit recognition

SOURCE: This is just a couple of decorations on a notebook published in databricks community edition in 2016.

Decision Trees for handwritten digit recognition

This notebook demonstrates learning a Decision Tree using Spark's distributed implementation. It gives the reader a better understanding of some critical hyperparameters for the tree learning algorithm, using examples to demonstrate how tuning the hyperparameters can improve accuracy.

Background: To learn more about Decision Trees, check out the resources at the end of this notebook. The visual description of ML and Decision Trees provides nice intuition helpful to understand this notebook, and Wikipedia gives lots of details.

Data: We use the classic MNIST handwritten digit recognition dataset. It is from LeCun et al. (1998) and may be found under "mnist" at the LibSVM dataset page.

Goal: Our goal for our data is to learn how to recognize digits (0 - 9) from images of handwriting. However, we will focus on understanding trees, not on this particular learning problem.

Takeaways: Decision Trees take several hyperparameters which can affect the accuracy of the learned model. There is no one "best" setting for these for all datasets. To get the optimal accuracy, we need to tune these hyperparameters based on our data.

Let's Build Intuition for Learning with Decision Trees

Load MNIST training and test datasets

Our datasets are vectors of pixels representing images of handwritten digits. For example:

Image of a digit Image of all 10 digits

These datasets are stored in the popular LibSVM dataset format. We will load them using MLlib's LibSVM dataset reader utility.

//-----------------------------------------------------------------------------------------------------------------
// using RDD-based MLlib - ok for Spark 1.x
// MLUtils.loadLibSVMFile returns an RDD.
//import org.apache.spark.mllib.util.MLUtils
//val trainingRDD = MLUtils.loadLibSVMFile(sc, "/databricks-datasets/mnist-digits/data-001/mnist-digits-train.txt")
//val testRDD = MLUtils.loadLibSVMFile(sc, "/databricks-datasets/mnist-digits/data-001/mnist-digits-test.txt")
// We convert the RDDs to DataFrames to use with ML Pipelines.
//val training = trainingRDD.toDF()
//val test = testRDD.toDF()
// Note: In Spark 1.6 and later versions, Spark SQL has a LibSVM data source.  The above lines can be simplified to:
//// val training = sqlContext.read.format("libsvm").load("/mnt/mllib/mnist-digits-csv/mnist-digits-train.txt")
//// val test = sqlContext.read.format("libsvm").load("/mnt/mllib/mnist-digits-csv/mnist-digits-test.txt")
//-----------------------------------------------------------------------------------------------------------------
val training = spark.read.format("libsvm")
                    .option("numFeatures", "780")
                    .load("/databricks-datasets/mnist-digits/data-001/mnist-digits-train.txt")

val test = spark.read.format("libsvm")
                    .option("numFeatures", "780")
                    .load("/databricks-datasets/mnist-digits/data-001/mnist-digits-test.txt")
// Cache data for multiple uses.
training.cache()
test.cache()

println(s"We have ${training.count} training images and ${test.count} test images.")
We have 60000 training images and 10000 test images.
training: org.apache.spark.sql.DataFrame = [label: double, features: vector]
test: org.apache.spark.sql.DataFrame = [label: double, features: vector]

Display our data. Each image has the true label (the label column) and a vector of features which represent pixel intensities (see below for details of what is in training).

training.printSchema()
root
 |-- label: double (nullable = true)
 |-- features: vector (nullable = true)
training.show(3) // replace 'true' by 'false' to see the whole row hidden by '...'
+-----+--------------------+
|label|            features|
+-----+--------------------+
|  5.0|(780,[152,153,154...|
|  0.0|(780,[127,128,129...|
|  4.0|(780,[160,161,162...|
+-----+--------------------+
only showing top 3 rows
display(training) // this is databricks-specific for interactive visual convenience

The pixel intensities are represented in features as a sparse vector, for example the first observation, as seen in row 1 of the output to display(training) or training.show(2,false) above, has label as 5, i.e. the hand-written image is for the number 5. And this hand-written image is the following sparse vector (just click the triangle to the left of the feature in first row to see the following):

type: 0
size: 780
indices: [152,153,155,...,682,683]
values: [3, 18, 18,18,126,...,132,16]

Here,

  • type: 0 says we have a sparse vector that only represents non-zero entries (as opposed to a dense vector where every entry is represented).
  • size: 780 says the vector has 780 indices in total
  • these indices from 0,...,779 are a unidimensional indexing of the two-dimensional array of pixels in the image
  • indices: [152,153,155,...,682,683] are the indices from the [0,1,...,779] possible indices with non-zero values
    • a value is an integer encoding the gray-level at the pixel index
  • values: [3, 18, 18,18,126,...,132,16] are the actual gray level values, for example:
    • at pixed index 152 the gray-level value is 3,
    • at index 153 the gray-level value is 18,
    • ..., and finally at
    • at index 683 the gray-level value is 18

Train a Decision Tree

We begin by training a decision tree using the default settings. Before training, we want to tell the algorithm that the labels are categories 0-9, rather than continuous values. We use the StringIndexer class to do this. We tie this feature preprocessing together with the tree algorithm using a Pipeline. ML Pipelines are tools Spark provides for piecing together Machine Learning algorithms into workflows. To learn more about Pipelines, check out other ML example notebooks in Databricks and the ML Pipelines user guide. Also See mllib-decision-tree.html#basic-algorithm.

// Import the ML algorithms we will use.
import org.apache.spark.ml.classification.{DecisionTreeClassifier, DecisionTreeClassificationModel}
import org.apache.spark.ml.feature.StringIndexer
import org.apache.spark.ml.Pipeline
import org.apache.spark.ml.classification.{DecisionTreeClassifier, DecisionTreeClassificationModel}
import org.apache.spark.ml.feature.StringIndexer
import org.apache.spark.ml.Pipeline
// StringIndexer: Read input column "label" (digits) and annotate them as categorical values.
val indexer = new StringIndexer().setInputCol("label").setOutputCol("indexedLabel")

// DecisionTreeClassifier: Learn to predict column "indexedLabel" using the "features" column.
val dtc = new DecisionTreeClassifier().setLabelCol("indexedLabel")

// Chain indexer + dtc together into a single ML Pipeline.
val pipeline = new Pipeline().setStages(Array(indexer, dtc))
indexer: org.apache.spark.ml.feature.StringIndexer = strIdx_cdb9fb742f94
dtc: org.apache.spark.ml.classification.DecisionTreeClassifier = dtc_9345fcaec0f5
pipeline: org.apache.spark.ml.Pipeline = pipeline_a426bd538000

Now, let's fit a model to our data.

val model = pipeline.fit(training)
model: org.apache.spark.ml.PipelineModel = pipeline_a426bd538000

We can inspect the learned tree by displaying it using Databricks ML visualization. (Visualization is available for several but not all models.)

// The tree is the last stage of the Pipeline.  Display it!
val tree = model.stages.last.asInstanceOf[DecisionTreeClassificationModel]
display(tree)
treeNode
{"index":31,"featureType":"continuous","prediction":null,"threshold":133.5,"categories":null,"feature":350,"overflow":false}
{"index":15,"featureType":"continuous","prediction":null,"threshold":0.5,"categories":null,"feature":568,"overflow":false}
{"index":7,"featureType":"continuous","prediction":null,"threshold":0.5,"categories":null,"feature":430,"overflow":false}
{"index":3,"featureType":"continuous","prediction":null,"threshold":2.5,"categories":null,"feature":405,"overflow":false}
{"index":1,"featureType":"continuous","prediction":null,"threshold":12.5,"categories":null,"feature":485,"overflow":false}
{"index":0,"featureType":null,"prediction":1.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":2,"featureType":null,"prediction":4.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":5,"featureType":"continuous","prediction":null,"threshold":14.5,"categories":null,"feature":516,"overflow":false}
{"index":4,"featureType":null,"prediction":9.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":6,"featureType":null,"prediction":7.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":11,"featureType":"continuous","prediction":null,"threshold":34.5,"categories":null,"feature":211,"overflow":false}
{"index":9,"featureType":"continuous","prediction":null,"threshold":0.5,"categories":null,"feature":98,"overflow":false}
{"index":8,"featureType":null,"prediction":8.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":10,"featureType":null,"prediction":6.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":13,"featureType":"continuous","prediction":null,"threshold":0.5,"categories":null,"feature":156,"overflow":false}
{"index":12,"featureType":null,"prediction":4.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":14,"featureType":null,"prediction":6.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":23,"featureType":"continuous","prediction":null,"threshold":0.5,"categories":null,"feature":435,"overflow":false}
{"index":19,"featureType":"continuous","prediction":null,"threshold":10.5,"categories":null,"feature":489,"overflow":false}
{"index":17,"featureType":"continuous","prediction":null,"threshold":2.5,"categories":null,"feature":380,"overflow":false}
{"index":16,"featureType":null,"prediction":5.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":18,"featureType":null,"prediction":9.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":21,"featureType":"continuous","prediction":null,"threshold":0.5,"categories":null,"feature":320,"overflow":false}
{"index":20,"featureType":null,"prediction":3.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":22,"featureType":null,"prediction":9.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":27,"featureType":"continuous","prediction":null,"threshold":0.5,"categories":null,"feature":346,"overflow":false}
{"index":25,"featureType":"continuous","prediction":null,"threshold":97.5,"categories":null,"feature":348,"overflow":false}
{"index":24,"featureType":null,"prediction":3.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":26,"featureType":null,"prediction":7.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":29,"featureType":"continuous","prediction":null,"threshold":0.5,"categories":null,"feature":655,"overflow":false}
{"index":28,"featureType":null,"prediction":6.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":30,"featureType":null,"prediction":7.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":47,"featureType":"continuous","prediction":null,"threshold":36.5,"categories":null,"feature":489,"overflow":false}
{"index":39,"featureType":"continuous","prediction":null,"threshold":26.5,"categories":null,"feature":290,"overflow":false}
{"index":35,"featureType":"continuous","prediction":null,"threshold":100.5,"categories":null,"feature":486,"overflow":false}
{"index":33,"featureType":"continuous","prediction":null,"threshold":129.5,"categories":null,"feature":490,"overflow":false}
{"index":32,"featureType":null,"prediction":2.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":34,"featureType":null,"prediction":0.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":37,"featureType":"continuous","prediction":null,"threshold":0.5,"categories":null,"feature":656,"overflow":false}
{"index":36,"featureType":null,"prediction":3.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":38,"featureType":null,"prediction":7.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":43,"featureType":"continuous","prediction":null,"threshold":5.5,"categories":null,"feature":297,"overflow":false}
{"index":41,"featureType":"continuous","prediction":null,"threshold":169.5,"categories":null,"feature":486,"overflow":false}
{"index":40,"featureType":null,"prediction":9.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":42,"featureType":null,"prediction":6.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":45,"featureType":"continuous","prediction":null,"threshold":0.5,"categories":null,"feature":598,"overflow":false}
{"index":44,"featureType":null,"prediction":4.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":46,"featureType":null,"prediction":7.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":55,"featureType":"continuous","prediction":null,"threshold":0.5,"categories":null,"feature":521,"overflow":false}
{"index":51,"featureType":"continuous","prediction":null,"threshold":7.5,"categories":null,"feature":347,"overflow":false}
{"index":49,"featureType":"continuous","prediction":null,"threshold":4.5,"categories":null,"feature":206,"overflow":false}
{"index":48,"featureType":null,"prediction":0.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":50,"featureType":null,"prediction":3.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":53,"featureType":"continuous","prediction":null,"threshold":16.5,"categories":null,"feature":514,"overflow":false}
{"index":52,"featureType":null,"prediction":4.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":54,"featureType":null,"prediction":7.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":59,"featureType":"continuous","prediction":null,"threshold":0.5,"categories":null,"feature":658,"overflow":false}
{"index":57,"featureType":"continuous","prediction":null,"threshold":8.5,"categories":null,"feature":555,"overflow":false}
{"index":56,"featureType":null,"prediction":6.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":58,"featureType":null,"prediction":3.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":61,"featureType":"continuous","prediction":null,"threshold":12.5,"categories":null,"feature":543,"overflow":false}
{"index":60,"featureType":null,"prediction":0.0,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":62,"featureType":null,"prediction":7.0,"threshold":null,"categories":null,"feature":null,"overflow":false}

Above, we can see how the tree makes predictions. When classifying a new example, the tree starts at the "root" node (at the top). Each tree node tests a pixel value and goes either left or right. At the bottom "leaf" nodes, the tree predicts a digit as the image's label.

Hyperparameter Tuning

Run the next cell and come back into hyper-parameter tuning for a couple minutes.

Exploring "maxDepth": training trees of different sizes

In this section, we test tuning a single hyperparameter maxDepth, which determines how deep (and large) the tree can be. We will train trees at varying depths and see how it affects the accuracy on our held-out test set.

Note: The next cell can take about 1 minute to run since it is training several trees which get deeper and deeper.

val variedMaxDepthModels = (0 until 8).map { maxDepth =>
  // For this setting of maxDepth, learn a decision tree.
  dtc.setMaxDepth(maxDepth)
  // Create a Pipeline with our feature processing stage (indexer) plus the tree algorithm
  val pipeline = new Pipeline().setStages(Array(indexer, dtc))
  // Run the ML Pipeline to learn a tree.
  pipeline.fit(training)
}
variedMaxDepthModels: scala.collection.immutable.IndexedSeq[org.apache.spark.ml.PipelineModel] = Vector(pipeline_e96074b3bded, pipeline_12646faf8260, pipeline_d5f639d6a180, pipeline_4034c9138161, pipeline_83215a1ed684, pipeline_8737125f5dcc, pipeline_02a6caa4d542, pipeline_88827be266ae)

We will use the default metric to evaluate the performance of our classifier:

// Define an evaluation metric.  In this case, we will use "accuracy".
import org.apache.spark.ml.evaluation.MulticlassClassificationEvaluator
val evaluator = new MulticlassClassificationEvaluator().setLabelCol("indexedLabel").setMetricName("f1") // default MetricName
import org.apache.spark.ml.evaluation.MulticlassClassificationEvaluator
evaluator: org.apache.spark.ml.evaluation.MulticlassClassificationEvaluator = MulticlassClassificationEvaluator: uid=mcEval_0ee0afcb7621, metricName=f1, metricLabel=0.0, beta=1.0, eps=1.0E-15
// For each maxDepth setting, make predictions on the test data, and compute the classifier's f1 performance metric.
val f1MetricPerformanceMeasures = (0 until 8).map { maxDepth =>
  val model = variedMaxDepthModels(maxDepth)
  // Calling transform() on the test set runs the fitted pipeline.
  // The learned model makes predictions on each test example.
  val predictions = model.transform(test)
  // Calling evaluate() on the predictions DataFrame computes our performance metric.
  (maxDepth, evaluator.evaluate(predictions))
}.toDF("maxDepth", "f1")
f1MetricPerformanceMeasures: org.apache.spark.sql.DataFrame = [maxDepth: int, f1: double]

We can display our accuracy results and see immediately that deeper, larger trees are more powerful classifiers, achieving higher accuracies.

Note: When you run f1MetricPerformanceMeasures.show(), you will get a table with f1 score getting better (i.e., approaching 1) with depth.

f1MetricPerformanceMeasures.show()
+--------+-------------------+
|maxDepth|                 f1|
+--------+-------------------+
|       0|  0.023138302649304|
|       1|0.07692344325297736|
|       2|0.21454218035530098|
|       3|0.43262516590643385|
|       4| 0.5918539983626627|
|       5| 0.6806954435278861|
|       6| 0.7478698562916142|
|       7| 0.7876393954574569|
+--------+-------------------+

Even though deeper trees are more powerful, they are not always better (recall from the SF/NYC city classification from house features at The visual description of ML and Decision Trees). If we kept increasing the depth on a rich enough dataset, training would take longer and longer. We also might risk overfitting (fitting the training data so well that our predictions get worse on test data); it is important to tune parameters based on held-out data to prevent overfitting. This will ensure that the fitted model generalizes well to yet unseen data, i.e. minimizes generalization error in a mathematical statistical sense.

Exploring "maxBins": discretization for efficient distributed computing

This section explores a more expert-level setting maxBins. For efficient distributed training of Decision Trees, Spark and most other libraries discretize (or "bin") continuous features (such as pixel values) into a finite number of values. This is an important step for the distributed implementation, but it introduces a tradeoff: Larger maxBins mean your data will be more accurately represented, but it will also mean more communication (and slower training).

The default value of maxBins generally works, but it is interesting to explore on our handwritten digit dataset. Remember our digit image from above:

Image of a digit

It is grayscale. But if we set maxBins = 2, then we are effectively making it a black-and-white image, not grayscale. Will that affect the accuracy of our model? Let's see!

Note: The next cell can take about 35 seconds to run since it trains several trees. Read the details on maxBins at mllib-decision-tree.html#split-candidates.

dtc.setMaxDepth(6) // Set maxDepth to a reasonable value.
// now try the maxBins "hyper-parameter" which actually acts as a "coarsener" 
//     mathematical researchers should note that it is a sub-algebra of the finite 
//     algebra of observable pixel images at the finest resolution available to us
// giving a compression of the image to fewer coarsely represented pixels
val f1MetricPerformanceMeasures = Seq(2, 4, 8, 16, 32).map { case maxBins =>
  // For this value of maxBins, learn a tree.
  dtc.setMaxBins(maxBins)
  val pipeline = new Pipeline().setStages(Array(indexer, dtc))
  val model = pipeline.fit(training)
  // Make predictions on test data, and compute accuracy.
  val predictions = model.transform(test)
  (maxBins, evaluator.evaluate(predictions))
}.toDF("maxBins", "f1")
f1MetricPerformanceMeasures: org.apache.spark.sql.DataFrame = [maxBins: int, f1: double]
f1MetricPerformanceMeasures.show()
+-------+------------------+
|maxBins|                f1|
+-------+------------------+
|      2|0.7429289482693366|
|      4|0.7390759023032782|
|      8|0.7443669963407805|
|     16|0.7426765688669141|
|     32|0.7478698562916142|
+-------+------------------+

We can see that extreme discretization (black and white) hurts performance as measured by F1-error, but only a bit. Using more bins increases the accuracy (but also makes learning more costly).

What's next?

  • Explore: Try out tuning other parameters of trees---or even ensembles like Random Forests or Gradient-Boosted Trees.
  • Automated tuning: This type of tuning does not have to be done by hand. (We did it by hand here to show the effects of tuning in detail.) MLlib provides automated tuning functionality via CrossValidator. Check out the other Databricks ML Pipeline guides or the Spark ML user guide for details.

Resources

If you are interested in learning more on these topics, these resources can get you started:

ScaDaMaLe Course site and book

Linear Algebra Review

This is a breeze'y scalarific break-down of:

Using the above resources we'll provide a review of basic linear algebra concepts that will recur throughout the course. These concepts include:

  • Matrices
  • Vectors
  • Arithmetic operations with vectors and matrices

We will see the accompanying Scala computations in the local or non-distributed setting.

Let's get a quick visual geometric interpretation for vectors, matrices and matrix-vector multiplications, eigen systems with real and comples Eigen values NOW from the following interactive visual-cognitive aid at:

Breeze is a linear algebra package in Scala. First, let us import it as follows:

import breeze.linalg._
import breeze.linalg._

1. Matrix: creation and element-access

A matrix is a two-dimensional array.

Let us denote matrices via bold uppercase letters as follows:

For instance, the matrix below is denoted with \(\mathbf{A}\), a capital bold A.

\[ \mathbf{A} = \begin{pmatrix} a_{11} & a_{12} & a_{13} \ a_{21} & a_{22} & a_{23} \ a_{31} & a_{32} & a_{33} \end{pmatrix} \]

We usually put commas between the row and column indexing sub-scripts, to make the possibly multi-digit indices distinguishable as follows:

\[ \mathbf{A} = \begin{pmatrix} a_{1,1} & a_{1,2} & a_{1,3} \ a_{2,1} & a_{2,2} & a_{2,3} \ a_{3,1} & a_{3,2} & a_{3,3} \end{pmatrix} \]

  • \(\mathbf{A}_{i,j}\) denotes the entry in \(i\)-th row and \(j\)-th column of the matrix \(\mathbf{A}\).
  • So for instance,
    • the first entry, the top left entry, is denoted by \(\mathbf{A}_{1,1}\).
    • And the entry in the third row and second column is denoted by \(\mathbf{A}_{3,2}\).
    • We say that a matrix with n rows and m columns is an \(n\) by \(m\) matrix and written as \(n \times m\)
      • The matrix \(\mathbf{A}\) shown above is a generic \(3 \times 3\) (pronounced 3-by-3) matrix.
      • And the matrix in Ameet's example in the video above, having 4 rows and 3 columns, is a 4 by 3 matrix.
    • If a matrix \(\mathbf{A}\) is \(n \times m\), we write:
      • \(\mathbf{A} \in \mathbb{R}^{n \times m}\) and say that \(\mathbf{A}\) is an \(\mathbb{R}\) to the power of the n times m,
        • where, \(\mathbb{R}\) here denotes the set of all real numbers in the line given by the open interval: \((-\infty,+\infty)\).

Let us created a matrix A as a val (that is immutable) in scala. The matrix we want to create is mathematically notated as follows:

\[ \mathbf{A} = \begin{pmatrix} a_{1,1} & a_{1,2} & a_{1,3} \ a_{2,1} & a_{2,2} & a_{2,3} \end{pmatrix}

\begin{pmatrix} 1 & 2 & 3 \ 4 & 5 & 6 \end{pmatrix} \]

val A = DenseMatrix((1, 2, 3), (4, 5, 6)) // let's create this 2 by 3 matrix
A: breeze.linalg.DenseMatrix[Int] =
1  2  3
4  5  6
A.size
res0: Int = 6
A.rows // number of rows
res1: Int = 2
A.size / A.rows // num of columns
res2: Int = 3
A.cols // also say
res3: Int = 3

Now, let's access the element \(a_{1,1}\), i.e., the element from the first row and first column of \(\mathbf{A}\), which in our val A matrix is the integer of type Int equalling 1.

A(0, 0) // Remember elements are indexed by zero in scala
res4: Int = 1

Gotcha: indices in breeze matrices start at 0 as in numpy of python and not at 1 as in MATLAB!

Of course if you assign the same dense matrix to a mutable var B then its entries can be modified as follows:

var B = DenseMatrix((1, 2, 3), (4, 5, 6))
B: breeze.linalg.DenseMatrix[Int] =
1  2  3
4  5  6
B(0,0)=999; B(1,1)=969; B(0,2)=666
B
res5: breeze.linalg.DenseMatrix[Int] =
999  2    666
4    969  6
  • A vector is a matrix with many rows and one column.

  • We'll denote a vector by bold lowercase letters: \[\mathbf{a} = \begin{pmatrix} 3.3 \ 1.0 \ 6.3 \ 3.6 \end{pmatrix}\]

    So, the vector above is denoted by \(\mathbf{a}\), the lowercase, bold a.

  • \(a_i\) denotes the i-th entry of a vector. So for instance:

    • \(a_2\) denotes the second entry of the vector and it is 1.0 for our vector.
  • If a vector is m-dimensional, then we say that \(\mathbf{a}\) is in \(\mathbb{R}^m\) and write \(\mathbf{a} \in \ \mathbb{R}^m\).

    • So our \(\mathbf{a} \in \ \mathbb{R}^4\).
val a = DenseVector(3.3, 1.0, 6.3, 3.6) // these are row vectors
a: breeze.linalg.DenseVector[Double] = DenseVector(3.3, 1.0, 6.3, 3.6)
a.size // a is a column vector of size 4
res6: Int = 4
a(1) // the second element of a is indexed by 1 as the first element is indexed by 0
res7: Double = 1.0
val a = DenseVector[Double](5, 4, -1) // this makes a vector of Doubles from input Int
a: breeze.linalg.DenseVector[Double] = DenseVector(5.0, 4.0, -1.0)
val a = DenseVector(5.0, 4.0, -1.0) // this makes a vector of Doubles from type inference . NOTE "5.0" is needed not just "5."
a: breeze.linalg.DenseVector[Double] = DenseVector(5.0, 4.0, -1.0)
val x = DenseVector.zeros[Double](5) // this will output x: breeze.linalg.DenseVector[Double] = DenseVector(0.0, 0.0, 0.0, 0.0, 0.0)
x: breeze.linalg.DenseVector[Double] = DenseVector(0.0, 0.0, 0.0, 0.0, 0.0)
val A = DenseMatrix((1, 4), (6, 1), (3, 5)) // let's create this 2 by 3 matrix
A: breeze.linalg.DenseMatrix[Int] =
1  4
6  1
3  5
A.t // transpose of A
res8: breeze.linalg.DenseMatrix[Int] =
1  6  3
4  1  5
val a = DenseVector(3.0, 4.0, 1.0)
a: breeze.linalg.DenseVector[Double] = DenseVector(3.0, 4.0, 1.0)
a.t
res9: breeze.linalg.Transpose[breeze.linalg.DenseVector[Double]] = Transpose(DenseVector(3.0, 4.0, 1.0))
val A = DenseMatrix((1, 4), (6, 1), (3, 5)) 
A: breeze.linalg.DenseMatrix[Int] =
1  4
6  1
3  5
val B = -A 
B: breeze.linalg.DenseMatrix[Int] =
-1  -4
-6  -1
-3  -5
A + B // should be A-A=0
res10: breeze.linalg.DenseMatrix[Int] =
0  0
0  0
0  0
A - B // should be A+A=2A
res11: breeze.linalg.DenseMatrix[Int] =
2   8
12  2
6   10
B - A // should be -A-A=-2A
res12: breeze.linalg.DenseMatrix[Int] =
-2   -8
-12  -2
-6   -10

Operators

All Tensors support a set of operators, similar to those used in Matlab or Numpy.

For HOMEWORK see: Workspace -> scalable-data-science -> xtraResources -> LinearAlgebra -> LAlgCheatSheet for a list of most of the operators and various operations.

Some of the basic ones are reproduced here, to give you an idea.

OperationBreezeMatlabNumpy
Elementwise additiona + ba + ba + b
Elementwise multiplicationa :* ba .* ba * b
Elementwise comparisona :< ba < b (gives matrix of 1/0 instead of true/false)a < b
Inplace additiona :+= 1.0a += 1a += 1
Inplace elementwise multiplicationa :*= 2.0a *= 2a *= 2
Vector dot producta dot b,a.t * bdot(a,b)dot(a,b)
Elementwise sumsum(a)sum(sum(a))a.sum()
Elementwise maxa.maxmax(a)a.max()
Elementwise argmaxargmax(a)argmax(a)a.argmax()
Ceilingceil(a)ceil(a)ceil(a)
Floorfloor(a)floor(a)floor(a)

Pop Quiz:

  • what is a natural geometric interpretation of scalar multiplication of a vector or a matrix and what about vector matrix multiplication?

Let's get a quick visual geometric interpretation for vectors, matrices and matrix-vector multiplications from the first interactive visual-cognitive aid at:

val A = DenseMatrix((1, 4), (6, 1), (3, 5)) 
A: breeze.linalg.DenseMatrix[Int] =
1  4
6  1
3  5
5 * A
res13: breeze.linalg.DenseMatrix[Int] =
5   20
30  5
15  25
A * 5
res14: breeze.linalg.DenseMatrix[Int] =
5   20
30  5
15  25
val A = DenseMatrix((1, 4), (6, 1), (3, 5)) 
A: breeze.linalg.DenseMatrix[Int] =
1  4
6  1
3  5
val B = DenseMatrix((3, 1), (2, 2), (1, 3)) 
B: breeze.linalg.DenseMatrix[Int] =
3  1
2  2
1  3
A *:* B // element-wise multiplication
res15: breeze.linalg.DenseMatrix[Int] =
3   4
12  2
3   15
val A = DenseMatrix((1, 4), (3, 1)) 
A: breeze.linalg.DenseMatrix[Int] =
1  4
3  1
val a = DenseVector(1, -1) // is a column vector
a: breeze.linalg.DenseVector[Int] = DenseVector(1, -1)
a.size // a is a column vector of size 2
res16: Int = 2
A * a
res17: breeze.linalg.DenseVector[Int] = DenseVector(-3, 2)
val A = DenseMatrix((1,2,3),(1,1,1))
A: breeze.linalg.DenseMatrix[Int] =
1  2  3
1  1  1
val B = DenseMatrix((4, 1), (9, 2), (8, 9))
B: breeze.linalg.DenseMatrix[Int] =
4  1
9  2
8  9
A*B // 4+18+14
res18: breeze.linalg.DenseMatrix[Int] =
46  32
21  12
1*4 + 2*9 + 3*8 // checking first entry of A*B
res19: Int = 46
val A = DenseMatrix((1,2,3),(4,5,6))
A: breeze.linalg.DenseMatrix[Int] =
1  2  3
4  5  6
DenseMatrix.eye[Int](3)
res20: breeze.linalg.DenseMatrix[Int] =
1  0  0
0  1  0
0  0  1
A * DenseMatrix.eye[Int](3)
res21: breeze.linalg.DenseMatrix[Int] =
1  2  3
4  5  6
DenseMatrix.eye[Int](2) * A
res22: breeze.linalg.DenseMatrix[Int] =
1  2  3
4  5  6
val D = DenseMatrix((2.0, 3.0), (4.0, 5.0))
val Dinv = inv(D)
D: breeze.linalg.DenseMatrix[Double] =
2.0  3.0
4.0  5.0
Dinv: breeze.linalg.DenseMatrix[Double] =
-2.5  1.5
2.0   -1.0
D * Dinv
res23: breeze.linalg.DenseMatrix[Double] =
1.0  0.0
0.0  1.0
Dinv * D
res24: breeze.linalg.DenseMatrix[Double] =
1.0  0.0
0.0  1.0
val b = DenseVector(4, 3)
norm(b)
b: breeze.linalg.DenseVector[Int] = DenseVector(4, 3)
res25: Double = 5.0
Math.sqrt(4*4 + 3*3) // check
res26: Double = 5.0

HOMEWORK: read this! https://github.com/scalanlp/breeze/wiki/Quickstart

It is here in markdown'd via wget and pandoc for your convenience.

Scala / nlp / breeze / Quickstart

David Hall edited this page on 24 Dec 2015

Breeze is modeled on Scala, and so if you're familiar with it, you'll be familiar with Breeze. First, import the linear algebra package:

scala> import breeze.linalg._

Let's create a vector:

scala> val x = DenseVector.zeros[Double](5)
x: breeze.linalg.DenseVector[Double] = DenseVector(0.0, 0.0, 0.0, 0.0, 0.0)

Here we make a column vector of zeros of type Double. And there are other ways we could create the vector - such as with a literal DenseVector(1,2,3) or with a call to fill or tabulate. The vector is "dense" because it is backed by an Array[Double], but could as well have created a SparseVector.zeros[Double](5), which would not allocate memory for zeros.

Unlike Scalala, all Vectors are column vectors. Row vectors are represented as Transpose[Vector[T]].

The vector object supports accessing and updating data elements by their index in 0 to x.length-1. Like Numpy, negative indices are supported, with the semantics that for an index i < 0 we operate on the i-th element from the end (x(i) == x(x.length + i)).

scala> x(0)
Double = 0.0

scala> x(1) = 2

scala> x
breeze.linalg.DenseVector[Double] = DenseVector(0.0, 2.0, 0.0, 0.0, 0.0)

Breeze also supports slicing. Note that slices using a Range are much, much faster than those with an arbitrary sequence.

scala> x(3 to 4) := .5
breeze.linalg.DenseVector[Double] = DenseVector(0.5, 0.5)

scala> x
breeze.linalg.DenseVector[Double] = DenseVector(0.0, 2.0, 0.0, 0.5, 0.5)

The slice operator constructs a read-through and write-through view of the given elements in the underlying vector. You set its values using the vectorized-set operator :=. You could as well have set it to a compatibly sized Vector.

scala> x(0 to 1) := DenseVector(.1,.2)

scala> x
breeze.linalg.DenseVector[Double] = DenseVector(0.1, 0.2, 0.0, 0.5, 0.5)

Similarly, a DenseMatrix can be created with a constructor method call, and its elements can be accessed and updated.

scala> val m = DenseMatrix.zeros[Int](5,5)
m: breeze.linalg.DenseMatrix[Int] = 
0  0  0  0  0  
0  0  0  0  0  
0  0  0  0  0  
0  0  0  0  0  
0  0  0  0  0  

The columns of m can be accessed as DenseVectors, and the rows as DenseMatrices.

scala> (m.rows, m.cols)
(Int, Int) = (5,5)

scala> m(::,1)
breeze.linalg.DenseVector[Int] = DenseVector(0, 0, 0, 0, 0)

scala>  m(4,::) := DenseVector(1,2,3,4,5).t  // transpose to match row shape
breeze.linalg.DenseMatrix[Int] = 1  2  3  4  5 

scala> m
breeze.linalg.DenseMatrix[Int] = 
0  0  0  0  0  
0  0  0  0  0  
0  0  0  0  0  
0  0  0  0  0  
1  2  3  4  5   

Assignments with incompatible cardinality or a larger numeric type won't compile.

scala> m := x
<console>:13: error: could not find implicit value for parameter op: breeze.linalg.operators.BinaryUpdateOp[breeze.linalg.DenseMatrix[Int],breeze.linalg.DenseVector[Double],breeze.linalg.operators.OpSet]
              m := x
                ^

Assignments with incompatible size will throw an exception:

scala> m := DenseMatrix.zeros[Int](3,3)
java.lang.IllegalArgumentException: requirement failed: Matrices must have same number of row

Sub-matrices can be sliced and updated, and literal matrices can be specified using a simple tuple-based syntax. Unlike Scalala, only range slices are supported, and only the columns (or rows for a transposed matrix) can have a Range step size different from 1.

scala> m(0 to 1, 0 to 1) := DenseMatrix((3,1),(-1,-2)) 
breeze.linalg.DenseMatrix[Int] = 
3   1   
-1  -2  

scala> m
breeze.linalg.DenseMatrix[Int] = 
3   1   0  0  0  
-1  -2  0  0  0  
0   0   0  0  0  
0   0   0  0  0  
1   2   3  4  5  

Broadcasting

Sometimes we want to apply an operation to every row or column of a matrix, as a unit. For instance, you might want to compute the mean of each row, or add a vector to every column. Adapting a matrix so that operations can be applied column-wise or row-wise is called broadcasting. Languages like R and numpy automatically and implicitly do broadcasting, meaning they won't stop you if you accidentally add a matrix and a vector. In Breeze, you have to signal your intent using the broadcasting operator *. The * is meant to evoke "foreach" visually. Here are some examples:

scala> import breeze.stats.mean

scala> val dm = DenseMatrix((1.0,2.0,3.0),
                            (4.0,5.0,6.0))

scala> val res = dm(::, *) + DenseVector(3.0, 4.0)
breeze.linalg.DenseMatrix[Double] =
4.0  5.0  6.0
8.0  9.0  10.0

scala> res(::, *) := DenseVector(3.0, 4.0)

scala> res
breeze.linalg.DenseMatrix[Double] =
3.0  3.0  3.0
4.0  4.0  4.0

scala> mean(dm(*, ::))
breeze.linalg.DenseVector[Double] = DenseVector(2.0, 5.0)

breeze.stats.distributions

Breeze also provides a fairly large number of probability distributions. These come with access to probability density function for either discrete or continuous distributions. Many distributions also have methods for giving the mean and the variance.

scala> import breeze.stats.distributions._

scala> val poi = new Poisson(3.0);
poi: breeze.stats.distributions.Poisson = <function1>

scala> val s = poi.sample(5);
s: IndexedSeq[Int] = Vector(5, 4, 5, 7, 4)

scala> s map { poi.probabilityOf(_) }
IndexedSeq[Double] = Vector(0.10081881344492458, 0.16803135574154085, 0.10081881344492458, 0.02160403145248382, 0.16803135574154085)

scala> val doublePoi = for(x <- poi) yield x.toDouble // meanAndVariance requires doubles, but Poisson samples over Ints
doublePoi: breeze.stats.distributions.Rand[Double] = breeze.stats.distributions.Rand$$anon$11@1b52e04

scala> breeze.stats.meanAndVariance(doublePoi.samples.take(1000));
breeze.stats.MeanAndVariance = MeanAndVariance(2.9960000000000067,2.9669509509509533,1000)

scala> (poi.mean,poi.variance)
(Double, Double) = (3.0,3.0)

NOTE: Below, there is a possibility of confusion for the term rate in the family of exponential distributions. Breeze parameterizes the distribution with the mean, but refers to it as the rate.

scala> val expo = new Exponential(0.5);
expo: breeze.stats.distributions.Exponential = Exponential(0.5)

scala> expo.rate
Double = 0.5

A characteristic of exponential distributions is its half-life, but we can compute the probability a value falls between any two numbers.

scala> expo.probability(0, log(2) * expo.rate)
Double = 0.5

scala> expo.probability(0.0, 1.5)
Double = 0.950212931632136

This means that approximately 95% of the draws from an exponential distribution fall between 0 and thrice the mean. We could have easily computed this with the cumulative distribution as well

scala> 1 - exp(-3.0)
Double = 0.950212931632136


scala> val samples = expo.sample(2).sorted;
samples: IndexedSeq[Double] = Vector(1.1891135726280517, 2.325607782657507)

scala> expo.probability(samples(0), samples(1));
Double = 0.08316481553047272

scala> breeze.stats.meanAndVariance(expo.samples.take(10000));
breeze.stats.MeanAndVariance = MeanAndVariance(2.029351863973081,4.163267835527843,10000)

scala> (1 / expo.rate, 1 / (expo.rate * expo.rate))
(Double, Double) = (2.0,4.0)

breeze.optimize

TODO: document breeze.optimize.minimize, recommend that instead.

Breeze's optimization package includes several convex optimization routines and a simple linear program solver. Convex optimization routines typically take a DiffFunction[T], which is a Function1 extended to have a gradientAt method, which returns the gradient at a particular point. Most routines will require a breeze.linalg-enabled type: something like a Vector or a Counter.

Here's a simple DiffFunction: a parabola along each vector's coordinate.

scala> import breeze.optimize._

scala>  val f = new DiffFunction[DenseVector[Double]] {
     |               def calculate(x: DenseVector[Double]) = {
     |                 (norm((x - 3d) :^ 2d,1d),(x * 2d) - 6d);
     |               }
     |             }
f: java.lang.Object with breeze.optimize.DiffFunction[breeze.linalg.DenseVector[Double]] = $anon$1@617746b2

Note that this function takes its minimum when all values are 3. (It's just a parabola along each coordinate.)

scala> f.valueAt(DenseVector(3,3,3))
Double = 0.0

scala> f.gradientAt(DenseVector(3,0,1))
breeze.linalg.DenseVector[Double] = DenseVector(0.0, -6.0, -4.0)

scala>  f.calculate(DenseVector(0,0))
(Double, breeze.linalg.DenseVector[Double]) = (18.0,DenseVector(-6.0, -6.0))

You can also use approximate derivatives, if your function is easy enough to compute:

scala> def g(x: DenseVector[Double]) = (x - 3.0):^ 2.0 sum

scala> g(DenseVector(0.,0.,0.))
Double = 27.0

scala> val diffg = new ApproximateGradientFunction(g)

scala> diffg.gradientAt(DenseVector(3,0,1))
breeze.linalg.DenseVector[Double] = DenseVector(1.000000082740371E-5, -5.999990000127297, -3.999990000025377)

Ok, now let's optimize f. The easiest routine to use is just LBFGS, which is a quasi-Newton method that works well for most problems.

scala> val lbfgs = new LBFGS[DenseVector[Double]](maxIter=100, m=3) // m is the memory. anywhere between 3 and 7 is fine. The larger m, the more memory is needed.

scala> val optimum = lbfgs.minimize(f,DenseVector(0,0,0))
optimum: breeze.linalg.DenseVector[Double] = DenseVector(2.9999999999999973, 2.9999999999999973, 2.9999999999999973)

scala> f(optimum)
Double = 2.129924444096732E-29

That's pretty close to 0! You can also use a configurable optimizer, using FirstOrderMinimizer.OptParams. It takes several parameters:

case class OptParams(batchSize:Int = 512,
                     regularization: Double = 1.0,
                     alpha: Double = 0.5,
                     maxIterations:Int = -1,
                     useL1: Boolean = false,
                     tolerance:Double = 1E-4,
                     useStochastic: Boolean= false) {
  // ...
}

batchSize applies to BatchDiffFunctions, which support using small minibatches of a dataset. regularization integrates L2 or L1 (depending on useL1) regularization with constant lambda. alpha controls the initial stepsize for algorithms that need it. maxIterations is the maximum number of gradient steps to be taken (or -1 for until convergence). tolerance controls the sensitivity of the convergence check. Finally, useStochastic determines whether or not batch functions should be optimized using a stochastic gradient algorithm (using small batches), or using LBFGS (using the entire dataset).

OptParams can be controlled using breeze.config.Configuration, which we described earlier.

breeze.optimize.linear

We provide a DSL for solving linear programs, using Apache's Simplex Solver as the backend. This package isn't industrial strength yet by any means, but it's good for simple problems. The DSL is pretty simple:

import breeze.optimize.linear._
val lp = new LinearProgram()
import lp._
val x0 = Real()
val x1 = Real()
val x2 = Real()

val lpp =  ( (x0 +  x1 * 2 + x2 * 3 )
    subjectTo ( x0 * -1 + x1 + x2 <= 20)
    subjectTo ( x0 - x1 * 3 + x2 <= 30)
    subjectTo ( x0 <= 40 )
)

val result = maximize( lpp)

assert( norm(result.result - DenseVector(40.0,17.5,42.5), 2) < 1E-4)

We also have specialized routines for bipartite matching (KuhnMunkres and CompetitiveLinking) and flow problems.

Where to go next?

After reading this quickstart, you can go to other wiki pages, especially Linear Algebra Cheat-Sheet and Data Structures.

Review the following for example:

if you have not experienced or forgotten big-O and big-Omega and big-Theta notation to study the computational efficiency of algorithms.

ScaDaMaLe Course site and book

Let us visit an interactive visual cognitive tool for the basics ideas in linear regression:

Linear Regression by Hastie and Tibshirani

Chapter 3 of https://www.dataschool.io/15-hours-of-expert-machine-learning-videos/

The following video playlist is a very concise and thorough treatment of linear regression for those who have taken the 200-level linear algebra. Others can fully understand it with some effort and revisiting.

Linear Regression PlayList

Ridge regression has a Bayesian interpretation where the weights have a zero-mean Gaussian prior. See 7.5 in Murphy's Machine Learning: A Probabilistic Perspective for details.

Please take notes in mark-down if you want.

For latex math within markdown you can do the following for in-line maths: \(\mathbf{A}_{i,j} \in \mathbb{R}^1\). And to write maths in display mode do the following:

\[\mathbf{A} \in \mathbb{R}^{m \times d} \]

You will need to write such notes for your final project presentation!

Getting our hands dirty with Darren Wilkinson's blog on regression

Let's follow the exposition in:

You need to scroll down the fitst link embedded in iframe below to get to the section on Analysis of quantitative data with Descriptive statistics and Linear regression sub-sections (you can skip the earlier part that shows you how to run everything locally in spark-shell - try this on your own later).

Let's do this live now...

import breeze.stats.distributions._
def x = Gaussian(1.0,2.0).sample(10000)
val xRdd = sc.parallelize(x)
import breeze.stats.distributions._
x: IndexedSeq[Double]
xRdd: org.apache.spark.rdd.RDD[Double] = ParallelCollectionRDD[0] at parallelize at command-2971213210277124:3
println(xRdd.mean)
println(xRdd.sampleVariance)
0.9961211853107911
4.025384520599017
val xStats = xRdd.stats
xStats.mean
xStats.sampleVariance
xStats.sum
xStats: org.apache.spark.util.StatCounter = (count: 10000, mean: 0.996121, stdev: 2.006236, max: 8.326542, min: -6.840659)
res1: Double = 9961.21185310791
val x2 = Gaussian(0.0,1.0).sample(10000) // 10,000 Gaussian samples with mean 0.0 and std dev 1.0
val xx = x zip x2 // creating tuples { (x,x2)_1, ... , (x,x2)_10000}
val lp = xx map {p => 2.0*p._1 + 1.0*p._2 + 1.5} // { lp_i := (2.0*x + 1.0 * x2 + 1.5)_i, i=1,...,10000 }
val eps = Gaussian(0.0,1.0).sample(10000) // standrad normal errors
val y = (lp zip eps) map (p => p._1 + p._2)
val yx = (y zip xx) map (p => (p._1, p._2._1, p._2._2))
x2: IndexedSeq[Double] = Vector(0.1510498720110515, -0.21709023201809416, -0.9420189342233366, -0.6050521762158899, 0.48771393128636853, 0.027986752952643124, 0.08206698908429294, -0.7810931162704136, -1.2057806605697985, -0.9176042669882863, 1.1959113751272468, 0.5771223111098949, -0.5030579509564024, 0.05792512611966754, 2.0492117764647917, -1.6192400586380957, -0.28568171141353893, 1.662660432138664, -0.3053683539449641, 0.3879563181609168, -0.7733054017369991, -0.39556455561853454, 1.7717311537878704, 0.33232937623812936, -0.1392031424321576, -0.5587152832826312, -1.7575839385785728, -0.6579581256900572, 2.037190332203657, 0.03462069676057432, -0.3795037160416964, 0.4622268686186779, -1.0897313199516543, -1.6880936202156007, -0.19374927120525648, -0.5509651353004006, -1.7588836379571422, -0.28930357427256465, 0.4020360571731675, -1.6301541413671794, 0.5958281089725639, 0.366330814768569, 0.4073858014158006, 0.16855406345881346, -0.947375008877488, -1.301502215739479, 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(-2.9824782737280255,1.0721139408861649), (1.559154053243073,-0.7709696933298915), (1.7355575197273223,1.4262689270118047), (1.11638805377925,0.008052693380149429), (4.6951872993892,-0.7675924241217212), (2.737373852455214,-0.875355770610139), (-1.151456200240173,0.3318552144813144), (3.0152094819448543,0.47230162167225975), (2.0959843639444466,-0.28845007593399613), (0.33596546387727444,0.33674053005607557), (1.040331737541483,-1.2685836846998517), (2.431166696911837,0.9973713512813284), (2.230055598607015,-0.14095584542177128), (1.3700666149073755,0.6434211266970435), (-0.4327077332358864,-1.3166935231718915), (-1.6077594316454586,0.5010874593219053), (-2.3718964441684305,0.5400322253256449), (2.6760922672748455,0.1131615290866549), (1.460158508062642,1.1948743843705798), (4.289535800486267,-0.4068064171361299), (0.7168408537080622,-0.2145531753251343), (-0.354296028077995,-0.8414414845064078), (0.6348900562033981,-0.17448661922809763), (4.50175610250241,0.015039956542559319), (4.007289452214197,-2.00225473143416), (0.5029484622378626,0.7768533690748148), (1.6705288530684772,0.7280781053306761), (-1.9266086884168034,-0.6814357844622568), (0.6563298284821315,2.4398143015234925), (3.8936524199780114,-1.9715384636473667), (-0.5323653052192214,-1.089089720589046), (-2.187378645730113,-1.0771030789727833), (1.4490595169584695,-1.1187887124853761), (-4.570489383235827,0.26304747184316635), (0.15125945754562187,0.6104069218328998), (3.502660482621176,0.814212432670669), (-0.7485242949055997,-1.1311163095796626), (3.5175847260522777,-0.715657837824097), (1.292722602559689,0.11337791560485909), (-1.0688535529107246,1.1903117127474667), (2.610918918455355,0.8655118045637775), (2.165592336786331,-0.4786300318354617), (3.2180039450399307,1.1374241148097717), (2.3110620837831366,1.3574248394663742), (-1.2620670074181475,-0.59796895966422), (-2.022658500226865,0.5787074373907313), (0.4225942665282606,-1.4837192620796162), (-1.8746483642338414,0.15009771866713956), (1.3304121456690439,-1.0785198355458125), (2.528499056420297,0.43654174540174034), (-2.5920035883882417,1.367374206941478), (1.8434672245723738,1.1624833124548457), (2.099308858628433,1.4378845237950593), (-0.8157539314263724,-0.4752367281036082), (-0.5844201825108297,-0.6295231876858187), (3.6001251647036625,0.13609988490474167), (0.9750494830689591,1.451172421854568), (-1.591208358857827,-0.9690521636819287), (2.272688328123594,-0.4657652028114279), (1.088984838199552,-0.3272245138051527), (2.700650297482846,-0.3254730682226242), (0.29059088340060446,-1.1968451698216205), (-0.8790370032378447,-2.374605096166881), (4.604279856177609,1.4231065460066927), (2.722449227993615,0.3339627050188421), (3.587573251254368,-0.37529586334821136), (-1.4412229896551314,1.7121288810552737), (2.0753371457353946,0.7740341080806812), (1.1111154091929833,-0.08101997848273264), (1.7671887536692417,0.8171553719668059), (1.9408459883070575,1.004037394973044), (0.7804144409892885,0.22996069331921015), (-1.8543998116282898,-0.135350519278533), (6.042636547872292,-0.4727403129550938), (2.1280007672692847,-0.1182151974084787), (0.4471612263594835,-1.9468945045910213), (1.2505523478947802,0.4579087802822954), (0.6984945299477181,1.3836409234546432), (-0.8471775601094396,0.02325932498935564), (4.322477962324404,0.475495388508411), (1.4341612180258405,-0.37698432805620236), (6.239615258142803,-0.8219848732487407), (-3.1535278213087903,-1.3951694203634668), (-0.463940144432212,0.0484490852454009), (-0.14771318640324793,0.9222291689334502), (0.20282785933721803,1.5679464498188418), (1.8482316809367179,0.810147143385619), (1.464243976509526,1.9186942393210789), (-2.344895033686407,-0.2176761309409645), (-0.6222382474654642,1.497682278641026), (-2.028256489351115,-0.6745280698091511), (-1.8185091579263823,-0.14287398549911423), (0.7775757995485517,-0.6123313834457077), (2.208419884574348,0.5533479535312111), (-1.510931362400885,0.17525285583058028), (0.15702274793503757,0.26417401560092896), (-0.460045243107128,0.7989612854266647), (3.543882315893044,-0.6531854416899909), (1.1358671646312586,0.3890137678570137), (1.0004036793674747,1.5942398929174109), (-2.229985885404819,0.29843502966443813), (0.27723413696937793,0.28270288452527464), (-1.0586523471937253,-1.030296515196584), (-0.6053699726992356,0.29004278605641326), (-0.9059032244427896,1.1839066433022867), (0.30610586096155024,0.5617980143776449), (-1.1035109557285785,0.3177318190024553), (0.818395734988232,-0.17078152902760071), (1.2887245591289829,-0.4129031279462113), (3.228020724069559,1.6509715706618235), (0.6610048448754513,-0.27367425727559463), (1.5679633903647399,1.2450208243939591), (1.5877868046262307,1.4063428988232145), (1.9799774803293921,1.6639488103943056), (1.8297536930120843,0.4109699563209272), (-0.21778571324236595,-2.1509670233572784), (0.6433445252381844,0.2639495116581482), (-1.261874773876885,-0.9708523309574577), (-1.020712141743926,1.2588123216998128), (-0.942167556946186,-0.6395148239066109), (2.7320211668089156,-2.3731627585033115), (2.812558906168454,0.43524872907522616), (-0.056923496414450714,0.6328073362083871), (-0.6014131312820246,-0.2381862432808314), (-3.5196269653783325,0.40492896291344244), (-1.1067214502928073,-1.0527840343286374), (-0.4736116098154268,1.0689442908821987), (2.6403094933932953,0.789255581937264), (1.5982824524769197,1.1724902795494772), (-0.09123150857004858,1.2893390188349818), (0.3777640975590455,0.8926054903089587), (1.5757168418364564,1.4246842661952515), (-0.24202485980852528,0.21910907895561132), (4.589933486557021,0.34689263334132264), (-2.331742795642637,-0.5771627038699307), (1.0060513913917988,-0.04827308490054824), (-0.4295021770429881,-0.8361201294738408), (-0.21561647198666445,0.2776346366703466), (1.4993086132360396,-2.583216199463966), (1.0627822777545926,-0.5754336242709439), (-2.4095942089088482,-0.4740298729504418), (1.5975461609152366,0.45528050967309863), (2.1565799558529477,-0.937001723779216), (0.0962289023611611,0.12442585999261868), (2.7095641996945012,-1.037597020742512), (-0.9219208363686942,0.6656497732259127), (-1.0338058740520197,0.09718535082910094), (1.6364174103842437,0.472044663569549), (1.2274838964756027,0.01365815985041524), (-0.7303973452135653,0.21443946294874028), (1.6471043795729972,0.38540036725618015), (0.13612088488197083,0.7807770362857364), (-4.201610226957669,0.12940125757456059), (0.8225909001565422,-0.9556204076037894), (-0.9482388322224697,-1.0007190699745476), (-1.5523717842885172,-1.4238233782457508), (-1.4048827543540963,0.09834207753278863), (1.5338217310158921,-2.5447136959911605), (2.2987508128497063,0.1997331013963162), (-1.9069233483255275,1.2806574080505437), (-0.48017389975436475,0.9315316175761184), (3.708171200382932,-0.6394107818742375), (1.646362242992558,-1.4099227738716835), (5.344457888650813,-0.21682467720141205), (4.0401870066710455,-0.214248285713938...
val rddLR = sc.parallelize(yx)
rddLR.take(5)
rddLR: org.apache.spark.rdd.RDD[(Double, Double, Double)] = ParallelCollectionRDD[4] at parallelize at command-2971213210277128:1
res2: Array[(Double, Double, Double)] = Array((5.677461671611596,1.6983876233282715,0.1510498720110515), (6.5963106438672625,1.9306937118935266,-0.21709023201809416), (-6.457080480280965,-3.613579039093624,-0.9420189342233366), (5.725199404014689,1.4774128627063305,-0.6050521762158899), (5.2485124653727215,0.49536920319327216,0.48771393128636853))
val dfLR = rddLR.toDF("y","x1","x2")
dfLR.show
dfLR.show(5)
+-------------------+--------------------+--------------------+
|                  y|                  x1|                  x2|
+-------------------+--------------------+--------------------+
|  5.677461671611596|  1.6983876233282715|  0.1510498720110515|
| 6.5963106438672625|  1.9306937118935266|-0.21709023201809416|
| -6.457080480280965|  -3.613579039093624| -0.9420189342233366|
|  5.725199404014689|  1.4774128627063305| -0.6050521762158899|
| 5.2485124653727215| 0.49536920319327216| 0.48771393128636853|
|  6.147100844408568|   2.619266385545484|0.027986752952643124|
|-0.7268042607303868| -1.6216138344745752| 0.08206698908429294|
| 5.5363351738375695|  1.2511380715559544| -0.7810931162704136|
|-0.1828379004896784| -0.6891022233658615| -1.2057806605697985|
|  6.488199218865876|  2.7890847095863527| -0.9176042669882863|
| 1.3969322930903634| -0.8384317817611013|  1.1959113751272468|
|  1.468434023004454|-0.39702300426389736|  0.5771223111098949|
|-0.6234341966751746|-0.20341459413042506| -0.5030579509564024|
|  6.452061108539848|   1.940354690386933| 0.05792512611966754|
|  9.199371261060582|  3.1686700336304794|  2.0492117764647917|
|0.07256979343692907|-0.01571825151138...| -1.6192400586380957|
|  9.589528428542355|  3.5222633033548227|-0.28568171141353893|
| 1.1696257215909478| -1.7700416261712641|   1.662660432138664|
|-0.8138719762638745|  -1.276616299487233| -0.3053683539449641|
|  9.309926019422797|   2.847017612404211|  0.3879563181609168|
+-------------------+--------------------+--------------------+
only showing top 20 rows

+------------------+-------------------+--------------------+
|                 y|                 x1|                  x2|
+------------------+-------------------+--------------------+
| 5.677461671611596| 1.6983876233282715|  0.1510498720110515|
|6.5963106438672625| 1.9306937118935266|-0.21709023201809416|
|-6.457080480280965| -3.613579039093624| -0.9420189342233366|
| 5.725199404014689| 1.4774128627063305| -0.6050521762158899|
|5.2485124653727215|0.49536920319327216| 0.48771393128636853|
+------------------+-------------------+--------------------+
only showing top 5 rows

dfLR: org.apache.spark.sql.DataFrame = [y: double, x1: double ... 1 more field]
// importing for regression
import org.apache.spark.ml.regression.LinearRegression
import org.apache.spark.ml.linalg._

val lm = new LinearRegression
lm.explainParams
lm.getStandardization
lm.setStandardization(false)
lm.getStandardization
lm.explainParams
import org.apache.spark.ml.regression.LinearRegression
import org.apache.spark.ml.linalg._
lm: org.apache.spark.ml.regression.LinearRegression = linReg_fd18c4adb9af
res5: String =
aggregationDepth: suggested depth for treeAggregate (>= 2) (default: 2)
elasticNetParam: the ElasticNet mixing parameter, in range [0, 1]. For alpha = 0, the penalty is an L2 penalty. For alpha = 1, it is an L1 penalty (default: 0.0)
epsilon: The shape parameter to control the amount of robustness. Must be > 1.0. (default: 1.35)
featuresCol: features column name (default: features)
fitIntercept: whether to fit an intercept term (default: true)
labelCol: label column name (default: label)
loss: The loss function to be optimized. Supported options: squaredError, huber. (Default squaredError) (default: squaredError)
maxBlockSizeInMB: Maximum memory in MB for stacking input data into blocks. Data is stacked within partitions. If more than remaining data size in a partition then it is adjusted to the data size. Default 0.0 represents choosing optimal value, depends on specific algorithm. Must be >= 0. (default: 0.0)
maxIter: maximum number of iterations (>= 0) (default: 100)
predictionCol: prediction column name (default: prediction)
regParam: regularization parameter (>= 0) (default: 0.0)
solver: The solver algorithm for optimization. Supported options: auto, normal, l-bfgs. (Default auto) (default: auto)
standardization: whether to standardize the training features before fitting the model (default: true, current: false)
tol: the convergence tolerance for iterative algorithms (>= 0) (default: 1.0E-6)
weightCol: weight column name. If this is not set or empty, we treat all instance weights as 1.0 (undefined)
// Transform data frame to required format
val dflr = (dfLR map {row => (row.getDouble(0), 
           Vectors.dense(row.getDouble(1),row.getDouble(2)))}).
           toDF("label","features")
dflr.show(5)
+------------------+--------------------+
|             label|            features|
+------------------+--------------------+
| 5.677461671611596|[1.69838762332827...|
|6.5963106438672625|[1.93069371189352...|
|-6.457080480280965|[-3.6135790390936...|
| 5.725199404014689|[1.47741286270633...|
|5.2485124653727215|[0.49536920319327...|
+------------------+--------------------+
only showing top 5 rows

dflr: org.apache.spark.sql.DataFrame = [label: double, features: vector]
// Fit model
val fit = lm.fit(dflr)
fit.intercept
fit: org.apache.spark.ml.regression.LinearRegressionModel = LinearRegressionModel: uid=linReg_fd18c4adb9af, numFeatures=2
res8: Double = 1.4942320912612896
fit.coefficients
res9: org.apache.spark.ml.linalg.Vector = [1.9996093571014764,1.0144075351786204]
val summ = fit.summary
summ: org.apache.spark.ml.regression.LinearRegressionTrainingSummary = org.apache.spark.ml.regression.LinearRegressionTrainingSummary@b34e84f
summ.r2
res10: Double = 0.9436414660418528
summ.rootMeanSquaredError
res11: Double = 1.0026971017612039
summ.coefficientStandardErrors
res12: Array[Double] = Array(0.005018897596822849, 0.009968316877946075, 0.01123197045538135)
summ.pValues
res13: Array[Double] = Array(0.0, 0.0, 0.0)
summ.tValues
res14: Array[Double] = Array(398.4160502432455, 101.76317101464718, 133.03383384038267)
summ.predictions.show(5)
+------------------+--------------------+------------------+
|             label|            features|        prediction|
+------------------+--------------------+------------------+
| 5.677461671611596|[1.69838762332827...| 5.043570003209616|
|6.5963106438672625|[1.93069371189352...| 5.134647336087737|
|-6.457080480280965|[-3.6135790390936...|-6.687105473093168|
| 5.725199404014689|[1.47741286270633...| 3.834711189101326|
|5.2485124653727215|[0.49536920319327...|2.9795176720949392|
+------------------+--------------------+------------------+
only showing top 5 rows
summ.residuals.show(5)
+-------------------+
|          residuals|
+-------------------+
| 0.6338916684019802|
| 1.4616633077795251|
|0.23002499281220334|
|  1.890488214913363|
| 2.2689947932777823|
+-------------------+
only showing top 5 rows

This gives you more on doing generalised linear modelling in Scala. But let's go back to out pipeline using the power-plant data.

Exercise: Writing your own Spark program for the least squares fit

Your task is to use the syntactic sugar below to write your own linear regression function using reduce and broadcast operations

How would you write your own Spark program to find the least squares fit on the following 1000 data points in RDD rddLR, where the variable y is the response variable, and X1 and X2 are independent variables?

More precisely, find \(w_1, w_2\), such that,

\(\sum_{i=1}^{10} (w_1 X1_i + w_2 X2_i - y_i)^2\) is minimized.

Report \(w_1\), \(w_2\), and the Root Mean Square Error and submit code in Spark. Analyze the resulting algorithm in terms of all-to-all, one-to-all, and all-to-one communication patterns.

rddLR.count
res17: Long = 10000
rddLR.take(10)
res18: Array[(Double, Double, Double)] = Array((5.677461671611596,1.6983876233282715,0.1510498720110515), (6.5963106438672625,1.9306937118935266,-0.21709023201809416), (-6.457080480280965,-3.613579039093624,-0.9420189342233366), (5.725199404014689,1.4774128627063305,-0.6050521762158899), (5.2485124653727215,0.49536920319327216,0.48771393128636853), (6.147100844408568,2.619266385545484,0.027986752952643124), (-0.7268042607303868,-1.6216138344745752,0.08206698908429294), (5.5363351738375695,1.2511380715559544,-0.7810931162704136), (-0.1828379004896784,-0.6891022233658615,-1.2057806605697985), (6.488199218865876,2.7890847095863527,-0.9176042669882863))
val dfLR = rddLR.toDF("y","x1","x2")
dfLR.show(10)
+-------------------+-------------------+--------------------+
|                  y|                 x1|                  x2|
+-------------------+-------------------+--------------------+
|  5.677461671611596| 1.6983876233282715|  0.1510498720110515|
| 6.5963106438672625| 1.9306937118935266|-0.21709023201809416|
| -6.457080480280965| -3.613579039093624| -0.9420189342233366|
|  5.725199404014689| 1.4774128627063305| -0.6050521762158899|
| 5.2485124653727215|0.49536920319327216| 0.48771393128636853|
|  6.147100844408568|  2.619266385545484|0.027986752952643124|
|-0.7268042607303868|-1.6216138344745752| 0.08206698908429294|
| 5.5363351738375695| 1.2511380715559544| -0.7810931162704136|
|-0.1828379004896784|-0.6891022233658615| -1.2057806605697985|
|  6.488199218865876| 2.7890847095863527| -0.9176042669882863|
+-------------------+-------------------+--------------------+
only showing top 10 rows

dfLR: org.apache.spark.sql.DataFrame = [y: double, x1: double ... 1 more field]
rddLR.getNumPartitions
res21: Int = 2
rddLR.map( yx1x2 => (yx1x2._2, yx1x2._3, yx1x2._1) ).take(10)
res22: Array[(Double, Double, Double)] = Array((1.6983876233282715,0.1510498720110515,5.677461671611596), (1.9306937118935266,-0.21709023201809416,6.5963106438672625), (-3.613579039093624,-0.9420189342233366,-6.457080480280965), (1.4774128627063305,-0.6050521762158899,5.725199404014689), (0.49536920319327216,0.48771393128636853,5.2485124653727215), (2.619266385545484,0.027986752952643124,6.147100844408568), (-1.6216138344745752,0.08206698908429294,-0.7268042607303868), (1.2511380715559544,-0.7810931162704136,5.5363351738375695), (-0.6891022233658615,-1.2057806605697985,-0.1828379004896784), (2.7890847095863527,-0.9176042669882863,6.488199218865876))
import breeze.linalg.DenseVector
    val pts = rddLR.map( yx1x2 => DenseVector(yx1x2._2, yx1x2._3, yx1x2._1) ).cache
import breeze.linalg.DenseVector
pts: org.apache.spark.rdd.RDD[breeze.linalg.DenseVector[Double]] = MapPartitionsRDD[40] at map at command-2971213210277150:2

Now all we need to do is one-to-all and all-to-one broadcast of the gradient...

val w = DenseVector(0.0, 0.0, 0.0)
val w_bc = sc.broadcast(w)
val step = 0.1
val max_iter = 100

/*
YouTry: Fix the expressions for grad_w0, grad_w1 and grad_w2 to have w_bc.value be the same as that from ml lib's fit.coefficients
*/    
for (i <- 1 to max_iter) {
        val grad_w0 = pts.map(x => 2*(w_bc.value(0)*1.0 + w_bc.value(1)*x(0) + w_bc.value(2)*x(1) - x(2))*1.0).reduce(_+_)
        val grad_w1 = pts.map(x => 2*(w_bc.value(0)*1.0 + w_bc.value(1)*x(0) + w_bc.value(2)*x(1) - x(2))*x(0)).reduce(_+_)
        val grad_w2 = pts.map(x => 2*(w_bc.value(0)*1.0 + w_bc.value(1)*x(0) + w_bc.value(2)*x(1) - x(2))*x(1)).reduce(_+_)
        w_bc.value(0) = w_bc.value(0) - step*grad_w0
        w_bc.value(1) = w_bc.value(1) - step*grad_w1
        w_bc.value(2) = w_bc.value(2) - step*grad_w2
}
w: breeze.linalg.DenseVector[Double] = DenseVector(703602.5501372493, 2297216.693185762, 194396.78259181185)
w_bc: org.apache.spark.broadcast.Broadcast[breeze.linalg.DenseVector[Double]] = Broadcast(16)
step: Double = 0.1
max_iter: Int = 100
w_bc.value
res24: breeze.linalg.DenseVector[Double] = DenseVector(703602.5501372493, 2297216.693185762, 194396.78259181185)
fit.intercept
res25: Double = 1.4942320912612896
fit.coefficients
res26: org.apache.spark.ml.linalg.Vector = [1.9996093571014764,1.0144075351786204]

Computing each of the gradients requires an all-to-one communication (due to the .reduce(_+_)). There are two of these per iteration. Broadcasting the updated w_bc requires one to all communication.

ScaDaMaLe Course site and book

A more detailed deep dive

We will mostly be using ML algorithms already implemented in Spark's libraries and packages.

However, in order to innovate and devise new algorithms, we need to understand more about distributed linear algebra and optimisation algorithms.

  • read: http://arxiv.org/pdf/1509.02256.pdf (also see References and Appendix A).
  • and go through the notebooks prepended by '19x' on various Data Types for distributed linear algebra.

You may want to follow this course from Stanford for a guided deeper dive. * http://stanford.edu/~rezab/dao/ * see notes here: https://github.com/lamastex/scalable-data-science/blob/master/read/daosu.pdf

Communication Hierarchy

In addition to time and space complexity of an algorithm, in the distributed setting, we also need to take care of communication complexity.

Access rates fall sharply with distance.

  • roughly 50 x gap between reading from memory and reading from either disk or the network.

We must take this communication hierarchy into consideration when developing parallel and distributed algorithms.

Focusing on strategies to reduce communication costs.

  • access rates fall sharply with distance.
  • so this communication hierarchy needs to be accounted for when developing parallel and distributed algorithms.

Lessons:

  • parallelism makes our computation faster

  • but network communication slows us down

  • SOLUTION: perform parallel and in-memory computation.

  • Persisting in memory is a particularly attractive option when working with iterative algorithms that read the same data multiple times, as is the case in gradient descent.

  • Several machine learning algorithms are iterative!

  • Limits of multi-core scaling (powerful multicore machine with several CPUs, and a huge amount of RAM).

    • advantageous:
      • sidestep any network communication when working with a single multicore machine
      • can indeed handle fairly large data sets, and they're an attractive option in many settings.
    • disadvantages:
      • can be quite expensive (due to specialized hardware),
      • not as widely accessible as commodity computing nodes.
      • this approach does have scalability limitations, as we'll eventually hit a wall when the data grows large enough! This is not the case for a distributed environment (like the AWS EC2 cloud under the hood here).

Simple strategies for algorithms in a distributed setting: to reduce network communication, simply keep large objects local

  • In the big n, small d case for linear regression
    • we can solve the problem via a closed form solution.
    • And this requires us to communicate \(O(d)^2\) intermediate data.
    • the largest object in this example is our initial data, which we store in a distributed fashion and never communicate! This is a data parallel setting.
  • In the big n, big d case (n is the sample size and d is the number of features):
    • for linear regression.
      • we use gradient descent to iteratively train our model and are again in a data parallel setting.
      • At each iteration we communicate the current parameter vector \(w_i\) and the required \(O(d)\) communication is feasible even for fairly large d.
  • In the small n, small d case:
    • for ridge regression.
      • we can communicate the small data to all of the workers.
      • this is an example of a model parallel setting where we can train the model for each hyper-parameter in parallel.
  • Linear regression with big n and huge d is an example of both data and model parallelism.

In this setting, since our data is large, we must still store it across multiple machines. We can still use gradient descent, or stochastic variants of gradient descent to train our model, but we may not want to communicate the entire d dimensional parameter vector at each iteration, when we have 10s, or hundreds of millions of features. In this setting we often rely on sparsity to reduce the communication. So far we discussed how we can reduce communication by keeping large data local.

ScaDaMaLe Course site and book

This is an elaboration of the Apache Spark mllib-progamming-guide on mllib-data-types.

Overview

Data Types - MLlib Programming Guide

MLlib supports local vectors and matrices stored on a single machine, as well as distributed matrices backed by one or more RDDs. Local vectors and local matrices are simple data models that serve as public interfaces. The underlying linear algebra operations are provided by Breeze and jblas. A training example used in supervised learning is called a “labeled point” in MLlib.

Why are we going through the basic distributed linear algebra Data Types?

This is to get you to be able to directly use them in a project or to roll your own algorithms.

ScaDaMaLe Course site and book

This is an elaboration of the Apache Spark mllib-progamming-guide on mllib-data-types.

Overview

Data Types - MLlib Programming Guide

MLlib supports local vectors and matrices stored on a single machine, as well as distributed matrices backed by one or more RDDs. Local vectors and local matrices are simple data models that serve as public interfaces. The underlying linear algebra operations are provided by Breeze and jblas. A training example used in supervised learning is called a “labeled point” in MLlib.

Local vector in Scala

A local vector has integer-typed and 0-based indices and double-typed values, stored on a single machine.

MLlib supports two types of local vectors:

  • dense and
  • sparse.

A dense vector is backed by a double array representing its entry values, while a sparse vector is backed by two parallel arrays: indices and values.

For example, a vector (1.0, 0.0, 3.0) can be represented:

  • in dense format as [1.0, 0.0, 3.0] or
  • in sparse format as (3, [0, 2], [1.0, 3.0]), where 3 is the size of the vector.

The base class of local vectors is Vector, and we provide two implementations: DenseVector and SparseVector. We recommend using the factory methods implemented in Vectors to create local vectors. Refer to the Vector Scala docs and Vectors Scala docs for details on the API.

import org.apache.spark.mllib.linalg.{Vector, Vectors}

// Create a dense vector (1.0, 0.0, 3.0).
val dv: Vector = Vectors.dense(1.0, 0.0, 3.0)
import org.apache.spark.mllib.linalg.{Vector, Vectors}
dv: org.apache.spark.mllib.linalg.Vector = [1.0,0.0,3.0]
// Create a sparse vector (1.0, 0.0, 3.0) by specifying its indices and values corresponding to nonzero entries.
val sv1: Vector = Vectors.sparse(3, Array(0, 2), Array(1.0, 3.0))
sv1: org.apache.spark.mllib.linalg.Vector = (3,[0,2],[1.0,3.0])
// Create a sparse vector (1.0, 0.0, 3.0) by specifying its nonzero entries.
val sv2: Vector = Vectors.sparse(3, Seq((0, 1.0), (2, 3.0)))
sv2: org.apache.spark.mllib.linalg.Vector = (3,[0,2],[1.0,3.0])

Note: Scala imports scala.collection.immutable.Vector by default, so you have to import org.apache.spark.mllib.linalg.Vector explicitly to use MLlib’s Vector.

python: MLlib recognizes the following types as dense vectors:

  • NumPy’s array
  • Python’s list, e.g., [1, 2, 3]

and the following as sparse vectors:

We recommend using NumPy arrays over lists for efficiency, and using the factory methods implemented in Vectors to create sparse vectors.

Refer to the Vectors Python docs for more details on the API.

import numpy as np
import scipy.sparse as sps
from pyspark.mllib.linalg import Vectors

# Use a NumPy array as a dense vector.
dv1 = np.array([1.0, 0.0, 3.0])
# Use a Python list as a dense vector.
dv2 = [1.0, 0.0, 3.0]
# Create a SparseVector.
sv1 = Vectors.sparse(3, [0, 2], [1.0, 3.0])
# Use a single-column SciPy csc_matrix as a sparse vector.
sv2 = sps.csc_matrix((np.array([1.0, 3.0]), np.array([0, 2]), np.array([0, 2])), shape = (3, 1))
print (dv1)
print (dv2)
print (sv1)
print (sv2)
[1. 0. 3.]
[1.0, 0.0, 3.0]
(3,[0,2],[1.0,3.0])
  (0, 0)	1.0
  (2, 0)	3.0

ScaDaMaLe Course site and book

This is an elaboration of the Apache Spark mllib-progamming-guide on mllib-data-types.

Overview

Data Types - MLlib Programming Guide

MLlib supports local vectors and matrices stored on a single machine, as well as distributed matrices backed by one or more RDDs. Local vectors and local matrices are simple data models that serve as public interfaces. The underlying linear algebra operations are provided by Breeze and jblas. A training example used in supervised learning is called a “labeled point” in MLlib.

Labeled point in Scala

A labeled point is a local vector, either dense or sparse, associated with a label/response. In MLlib, labeled points are used in supervised learning algorithms.

We use a double to store a label, so we can use labeled points in both regression and classification.

For binary classification, a label should be either 0 (negative) or 1 (positive). For multiclass classification, labels should be class indices starting from zero: 0, 1, 2, ....

A labeled point is represented by the case class LabeledPoint.

Refer to the LabeledPoint Scala docs for details on the API.

//import first
import org.apache.spark.mllib.linalg.Vectors
import org.apache.spark.mllib.regression.LabeledPoint
import org.apache.spark.mllib.linalg.Vectors
import org.apache.spark.mllib.regression.LabeledPoint
// Create a labeled point with a "positive" label and a dense feature vector.
val pos = LabeledPoint(1.0, Vectors.dense(1.0, 0.0, 3.0))
pos: org.apache.spark.mllib.regression.LabeledPoint = (1.0,[1.0,0.0,3.0])
// Create a labeled point with a "negative" label and a sparse feature vector.
val neg = LabeledPoint(0.0, Vectors.sparse(3, Array(0, 2), Array(1.0, 3.0)))
neg: org.apache.spark.mllib.regression.LabeledPoint = (0.0,(3,[0,2],[1.0,3.0]))

Sparse data in Scala

It is very common in practice to have sparse training data. MLlib supports reading training examples stored in LIBSVM format, which is the default format used by LIBSVM and LIBLINEAR. It is a text format in which each line represents a labeled sparse feature vector using the following format:

label index1:value1 index2:value2 ...

where the indices are one-based and in ascending order. After loading, the feature indices are converted to zero-based.

MLUtils.loadLibSVMFile reads training examples stored in LIBSVM format.

Refer to the MLUtils Scala docs for details on the API.

import org.apache.spark.mllib.regression.LabeledPoint
import org.apache.spark.mllib.util.MLUtils
import org.apache.spark.rdd.RDD

//val examples: RDD[LabeledPoint] = MLUtils.loadLibSVMFile(sc, "data/mllib/sample_libsvm_data.txt") // from prog guide but no such data here - can wget from github 
import org.apache.spark.mllib.regression.LabeledPoint
import org.apache.spark.mllib.util.MLUtils
import org.apache.spark.rdd.RDD

Load MNIST training and test datasets

Our datasets are vectors of pixels representing images of handwritten digits. For example:

Image of a digit Image of all 10 digits

display(dbutils.fs.ls("/databricks-datasets/mnist-digits/data-001/mnist-digits-train.txt"))
path name size
dbfs:/databricks-datasets/mnist-digits/data-001/mnist-digits-train.txt mnist-digits-train.txt 6.9430283e7
val examples: RDD[LabeledPoint] = MLUtils.loadLibSVMFile(sc, "/databricks-datasets/mnist-digits/data-001/mnist-digits-train.txt")
examples: org.apache.spark.rdd.RDD[org.apache.spark.mllib.regression.LabeledPoint] = MapPartitionsRDD[3661] at map at MLUtils.scala:88
examples.take(1)
res1: Array[org.apache.spark.mllib.regression.LabeledPoint] = Array((5.0,(780,[152,153,154,155,156,157,158,159,160,161,162,163,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,231,232,233,234,235,236,237,238,239,240,241,260,261,262,263,264,265,266,268,269,289,290,291,292,293,319,320,321,322,347,348,349,350,376,377,378,379,380,381,405,406,407,408,409,410,434,435,436,437,438,439,463,464,465,466,467,493,494,495,496,518,519,520,521,522,523,524,544,545,546,547,548,549,550,551,570,571,572,573,574,575,576,577,578,596,597,598,599,600,601,602,603,604,605,622,623,624,625,626,627,628,629,630,631,648,649,650,651,652,653,654,655,656,657,676,677,678,679,680,681,682,683],[3.0,18.0,18.0,18.0,126.0,136.0,175.0,26.0,166.0,255.0,247.0,127.0,30.0,36.0,94.0,154.0,170.0,253.0,253.0,253.0,253.0,253.0,225.0,172.0,253.0,242.0,195.0,64.0,49.0,238.0,253.0,253.0,253.0,253.0,253.0,253.0,253.0,253.0,251.0,93.0,82.0,82.0,56.0,39.0,18.0,219.0,253.0,253.0,253.0,253.0,253.0,198.0,182.0,247.0,241.0,80.0,156.0,107.0,253.0,253.0,205.0,11.0,43.0,154.0,14.0,1.0,154.0,253.0,90.0,139.0,253.0,190.0,2.0,11.0,190.0,253.0,70.0,35.0,241.0,225.0,160.0,108.0,1.0,81.0,240.0,253.0,253.0,119.0,25.0,45.0,186.0,253.0,253.0,150.0,27.0,16.0,93.0,252.0,253.0,187.0,249.0,253.0,249.0,64.0,46.0,130.0,183.0,253.0,253.0,207.0,2.0,39.0,148.0,229.0,253.0,253.0,253.0,250.0,182.0,24.0,114.0,221.0,253.0,253.0,253.0,253.0,201.0,78.0,23.0,66.0,213.0,253.0,253.0,253.0,253.0,198.0,81.0,2.0,18.0,171.0,219.0,253.0,253.0,253.0,253.0,195.0,80.0,9.0,55.0,172.0,226.0,253.0,253.0,253.0,253.0,244.0,133.0,11.0,136.0,253.0,253.0,253.0,212.0,135.0,132.0,16.0])))

Display our data. Each image has the true label (the label column) and a vector of features which represent pixel intensities (see below for details of what is in training).

display(examples.toDF) // covert to DataFrame and display for convenient db visualization

The pixel intensities are represented in features as a sparse vector, for example the first observation, as seen in row 1 of the output to display(training) below, has label as 5, i.e. the hand-written image is for the number 5. And this hand-written image is the following sparse vector (just click the triangle to the left of the feature in first row to see the following):

type: 0
size: 780
indices: [152,153,155,...,682,683]
values: [3, 18, 18,18,126,...,132,16]

Here

  • type: 0 says we hve a sparse vector.
  • size: 780 says the vector has 780 indices in total
  • these indices from 0,...,779 are a unidimensional indexing of the two-dimensional array of pixels in the image
  • indices: [152,153,155,...,682,683] are the indices from the [0,1,...,779] possible indices with non-zero values
    • a value is an integer encoding the gray-level at the pixel index
  • values: [3, 18, 18,18,126,...,132,16] are the actual gray level values, for example:
    • at pixed index 152 the gray-level value is 3,
    • at index 153 the gray-level value is 18,
    • ..., and finally at
    • at index 683 the gray-level value is 18

We could also use the following method as done in notebook 016_* already.

val training = spark.read.format("libsvm")
                    .option("numFeatures", "780")
                    .load("/databricks-datasets/mnist-digits/data-001/mnist-digits-train.txt")
training: org.apache.spark.sql.DataFrame = [label: double, features: vector]
display(training)


Labeled point in Python

A labeled point is represented by LabeledPoint.

Refer to the LabeledPoint Python docs for more details on the API.

# import first
from pyspark.mllib.linalg import SparseVector
from pyspark.mllib.regression import LabeledPoint

# Create a labeled point with a positive label and a dense feature vector.
pos = LabeledPoint(1.0, [1.0, 0.0, 3.0])

# Create a labeled point with a negative label and a sparse feature vector.
neg = LabeledPoint(0.0, SparseVector(3, [0, 2], [1.0, 3.0]))

Sparse data in Python

MLUtils.loadLibSVMFile reads training examples stored in LIBSVM format.

Refer to the MLUtils Python docs for more details on the API.

from pyspark.mllib.util import MLUtils

# examples = MLUtils.loadLibSVMFile(sc, "data/mllib/sample_libsvm_data.txt") #from prog guide but no such data here - can wget from github 
examples = MLUtils.loadLibSVMFile(sc, "/databricks-datasets/mnist-digits/data-001/mnist-digits-train.txt")
examples.take(1)
res5: Array[org.apache.spark.mllib.regression.LabeledPoint] = Array((5.0,(780,[152,153,154,155,156,157,158,159,160,161,162,163,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,231,232,233,234,235,236,237,238,239,240,241,260,261,262,263,264,265,266,268,269,289,290,291,292,293,319,320,321,322,347,348,349,350,376,377,378,379,380,381,405,406,407,408,409,410,434,435,436,437,438,439,463,464,465,466,467,493,494,495,496,518,519,520,521,522,523,524,544,545,546,547,548,549,550,551,570,571,572,573,574,575,576,577,578,596,597,598,599,600,601,602,603,604,605,622,623,624,625,626,627,628,629,630,631,648,649,650,651,652,653,654,655,656,657,676,677,678,679,680,681,682,683],[3.0,18.0,18.0,18.0,126.0,136.0,175.0,26.0,166.0,255.0,247.0,127.0,30.0,36.0,94.0,154.0,170.0,253.0,253.0,253.0,253.0,253.0,225.0,172.0,253.0,242.0,195.0,64.0,49.0,238.0,253.0,253.0,253.0,253.0,253.0,253.0,253.0,253.0,251.0,93.0,82.0,82.0,56.0,39.0,18.0,219.0,253.0,253.0,253.0,253.0,253.0,198.0,182.0,247.0,241.0,80.0,156.0,107.0,253.0,253.0,205.0,11.0,43.0,154.0,14.0,1.0,154.0,253.0,90.0,139.0,253.0,190.0,2.0,11.0,190.0,253.0,70.0,35.0,241.0,225.0,160.0,108.0,1.0,81.0,240.0,253.0,253.0,119.0,25.0,45.0,186.0,253.0,253.0,150.0,27.0,16.0,93.0,252.0,253.0,187.0,249.0,253.0,249.0,64.0,46.0,130.0,183.0,253.0,253.0,207.0,2.0,39.0,148.0,229.0,253.0,253.0,253.0,250.0,182.0,24.0,114.0,221.0,253.0,253.0,253.0,253.0,201.0,78.0,23.0,66.0,213.0,253.0,253.0,253.0,253.0,198.0,81.0,2.0,18.0,171.0,219.0,253.0,253.0,253.0,253.0,195.0,80.0,9.0,55.0,172.0,226.0,253.0,253.0,253.0,253.0,244.0,133.0,11.0,136.0,253.0,253.0,253.0,212.0,135.0,132.0,16.0])))

ScaDaMaLe Course site and book

This is an elaboration of the Apache Spark mllib-progamming-guide on mllib-data-types.

Overview

Data Types - MLlib Programming Guide

MLlib supports local vectors and matrices stored on a single machine, as well as distributed matrices backed by one or more RDDs. Local vectors and local matrices are simple data models that serve as public interfaces. The underlying linear algebra operations are provided by Breeze and jblas. A training example used in supervised learning is called a “labeled point” in MLlib.

Local Matrix in Scala

A local matrix has integer-typed row and column indices and double-typed values, stored on a single machine. MLlib supports:

  • dense matrices, whose entry values are stored in a single double array in column-major order, and
  • sparse matrices, whose non-zero entry values are stored in the Compressed Sparse Column (CSC) format in column-major order.

For example, the following dense matrix: \[ \begin{pmatrix} 1.0 & 2.0 \\ 3.0 & 4.0 \\ 5.0 & 6.0 \end{pmatrix} \] is stored in a one-dimensional array [1.0, 3.0, 5.0, 2.0, 4.0, 6.0] with the matrix size (3, 2).

The base class of local matrices is Matrix, and we provide two implementations: DenseMatrix, and SparseMatrix. We recommend using the factory methods implemented in Matrices to create local matrices. Remember, local matrices in MLlib are stored in column-major order.

Refer to the Matrix Scala docs and Matrices Scala docs for details on the API.

Int.MaxValue // note the largest value an index can take
res0: Int = 2147483647
import org.apache.spark.mllib.linalg.{Matrix, Matrices}

// Create a dense matrix ((1.0, 2.0), (3.0, 4.0), (5.0, 6.0))
val dm: Matrix = Matrices.dense(3, 2, Array(1.0, 3.0, 5.0, 2.0, 4.0, 6.0))
import org.apache.spark.mllib.linalg.{Matrix, Matrices}
dm: org.apache.spark.mllib.linalg.Matrix =
1.0  2.0
3.0  4.0
5.0  6.0

Next, let us create the following sparse local matrix: \[ \begin{pmatrix} 9.0 & 0.0 \\ 0.0 & 8.0 \\ 0.0 & 6.0 \end{pmatrix} \]

// Create a sparse matrix ((9.0, 0.0), (0.0, 8.0), (0.0, 6.0))
val sm: Matrix = Matrices.sparse(3, 2, Array(0, 1, 3), Array(0, 2, 1), Array(9, 6, 8))
sm: org.apache.spark.mllib.linalg.Matrix =
3 x 2 CSCMatrix
(0,0) 9.0
(2,1) 6.0
(1,1) 8.0

Local Matrix in Python

The base class of local matrices is Matrix, and we provide two implementations: DenseMatrix, and SparseMatrix. We recommend using the factory methods implemented in Matrices to create local matrices. Remember, local matrices in MLlib are stored in column-major order.

Refer to the Matrix Python docs and Matrices Python docs for more details on the API.

from pyspark.mllib.linalg import Matrix, Matrices

# Create a dense matrix ((1.0, 2.0), (3.0, 4.0), (5.0, 6.0))
dm2 = Matrices.dense(3, 2, [1, 2, 3, 4, 5, 6])
dm2
# Create a sparse matrix ((9.0, 0.0), (0.0, 8.0), (0.0, 6.0))
sm = Matrices.sparse(3, 2, [0, 1, 3], [0, 2, 1], [9, 6, 8])
sm

ScaDaMaLe Course site and book

This is an elaboration of the Apache Spark mllib-progamming-guide on mllib-data-types.

Overview

Data Types - MLlib Programming Guide

MLlib supports local vectors and matrices stored on a single machine, as well as distributed matrices backed by one or more RDDs. Local vectors and local matrices are simple data models that serve as public interfaces. The underlying linear algebra operations are provided by Breeze and jblas. A training example used in supervised learning is called a “labeled point” in MLlib.

Distributed matrix in Scala

A distributed matrix has long-typed row and column indices and double-typed values, stored distributively in one or more RDDs.

It is very important to choose the right format to store large and distributed matrices. Converting a distributed matrix to a different format may require a global shuffle, which is quite expensive.

Three types of distributed matrices have been implemented so far.

  1. The basic type is called RowMatrix.
  • A RowMatrix is a row-oriented distributed matrix without meaningful row indices, e.g., a collection of feature vectors. It is backed by an RDD of its rows, where each row is a local vector.
  • We assume that the number of columns is not huge for a RowMatrix so that a single local vector can be reasonably communicated to the driver and can also be stored / operated on using a single node.
  • An IndexedRowMatrix is similar to a RowMatrix but with row indices, which can be used for identifying rows and executing joins.
  • A CoordinateMatrix is a distributed matrix stored in coordinate list (COO) format, backed by an RDD of its entries.

Note

The underlying RDDs of a distributed matrix must be deterministic, because we cache the matrix size. In general the use of non-deterministic RDDs can lead to errors.

Remark: there is a huge difference in the orders of magnitude between the maximum size of local versus distributed matrices!

print(Long.MaxValue.toDouble, Int.MaxValue.toDouble, Long.MaxValue.toDouble / Int.MaxValue.toDouble) // index ranges and ratio for local and distributed matrices

ScaDaMaLe Course site and book

This is an elaboration of the Apache Spark mllib-progamming-guide on mllib-data-types.

Overview

Data Types - MLlib Programming Guide

MLlib supports local vectors and matrices stored on a single machine, as well as distributed matrices backed by one or more RDDs. Local vectors and local matrices are simple data models that serve as public interfaces. The underlying linear algebra operations are provided by Breeze and jblas. A training example used in supervised learning is called a “labeled point” in MLlib.

RowMatrix in Scala

A RowMatrix is a row-oriented distributed matrix without meaningful row indices, backed by an RDD of its rows, where each row is a local vector. Since each row is represented by a local vector, the number of columns is limited by the integer range but it should be much smaller in practice.

A RowMatrix can be created from an RDD[Vector] instance. Then we can compute its column summary statistics and decompositions.

Refer to the RowMatrix Scala docs for details on the API.

import org.apache.spark.mllib.linalg.{Vector, Vectors}
import org.apache.spark.mllib.linalg.distributed.RowMatrix
import org.apache.spark.mllib.linalg.{Vector, Vectors}
import org.apache.spark.mllib.linalg.distributed.RowMatrix
val rows: RDD[Vector] = sc.parallelize(Array(Vectors.dense(12.0, -51.0, 4.0), Vectors.dense(6.0, 167.0, -68.0), Vectors.dense(-4.0, 24.0, -41.0))) // an RDD of local vectors
rows: org.apache.spark.rdd.RDD[org.apache.spark.mllib.linalg.Vector] = ParallelCollectionRDD[3670] at parallelize at command-2972105651606776:1
// Create a RowMatrix from an RDD[Vector].
val mat: RowMatrix = new RowMatrix(rows)
mat: org.apache.spark.mllib.linalg.distributed.RowMatrix = org.apache.spark.mllib.linalg.distributed.RowMatrix@75c66624
mat.rows.collect
res0: Array[org.apache.spark.mllib.linalg.Vector] = Array([12.0,-51.0,4.0], [6.0,167.0,-68.0], [-4.0,24.0,-41.0])
// Get its size.
val m = mat.numRows()
val n = mat.numCols()
m: Long = 3
n: Long = 3
// QR decomposition
val qrResult = mat.tallSkinnyQR(true)
qrResult: org.apache.spark.mllib.linalg.QRDecomposition[org.apache.spark.mllib.linalg.distributed.RowMatrix,org.apache.spark.mllib.linalg.Matrix] =
QRDecomposition(org.apache.spark.mllib.linalg.distributed.RowMatrix@34f5da4f,14.0  21.0                 -14.0
0.0   -174.99999999999997  70.00000000000001
0.0   0.0                  -35.000000000000014  )
qrResult.R
res1: org.apache.spark.mllib.linalg.Matrix =
14.0  21.0                 -14.0
0.0   -174.99999999999997  70.00000000000001
0.0   0.0                  -35.000000000000014


RowMatrix in Python

A RowMatrix can be created from an RDD of vectors.

Refer to the RowMatrix Python docs for more details on the API.

from pyspark.mllib.linalg.distributed import RowMatrix

# Create an RDD of vectors.
rows = sc.parallelize([[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]])

# Create a RowMatrix from an RDD of vectors.
mat = RowMatrix(rows)

# Get its size.
m = mat.numRows()  # 4
n = mat.numCols()  # 3
print (m,'x',n)

# Get the rows as an RDD of vectors again.
rowsRDD = mat.rows
4 x 3

ScaDaMaLe Course site and book

This is an elaboration of the Apache Spark mllib-progamming-guide on mllib-data-types.

Overview

Data Types - MLlib Programming Guide

MLlib supports local vectors and matrices stored on a single machine, as well as distributed matrices backed by one or more RDDs. Local vectors and local matrices are simple data models that serve as public interfaces. The underlying linear algebra operations are provided by Breeze and jblas. A training example used in supervised learning is called a “labeled point” in MLlib.

IndexedRowMatrix in Scala

An IndexedRowMatrix is similar to a RowMatrix but with meaningful row indices. It is backed by an RDD of indexed rows, so that each row is represented by its index (long-typed) and a local vector.

An IndexedRowMatrix can be created from an RDD[IndexedRow] instance, where IndexedRow is a wrapper over (Long, Vector). An IndexedRowMatrix can be converted to a RowMatrix by dropping its row indices.

Refer to the IndexedRowMatrix Scala docs for details on the API.

import org.apache.spark.mllib.linalg.{Vector, Vectors}
import org.apache.spark.mllib.linalg.distributed.{IndexedRow, IndexedRowMatrix, RowMatrix}
import org.apache.spark.mllib.linalg.{Vector, Vectors}
import org.apache.spark.mllib.linalg.distributed.{IndexedRow, IndexedRowMatrix, RowMatrix}
Vector(12.0, -51.0, 4.0) // note Vector is a scala collection
res0: scala.collection.immutable.Vector[Double] = Vector(12.0, -51.0, 4.0)
Vectors.dense(12.0, -51.0, 4.0) // while this is a mllib.linalg.Vector
res1: org.apache.spark.mllib.linalg.Vector = [12.0,-51.0,4.0]
val rows: RDD[IndexedRow] = sc.parallelize(Array(IndexedRow(2, Vectors.dense(1,3)), IndexedRow(4, Vectors.dense(4,5)))) // an RDD of indexed rows
rows: org.apache.spark.rdd.RDD[org.apache.spark.mllib.linalg.distributed.IndexedRow] = ParallelCollectionRDD[3685] at parallelize at command-2972105651607186:1
// Create an IndexedRowMatrix from an RDD[IndexedRow].
val mat: IndexedRowMatrix = new IndexedRowMatrix(rows)
mat: org.apache.spark.mllib.linalg.distributed.IndexedRowMatrix = org.apache.spark.mllib.linalg.distributed.IndexedRowMatrix@300e1e99
// Get its size.
val m = mat.numRows()
val n = mat.numCols()
m: Long = 5
n: Long = 2
// Drop its row indices.
val rowMat: RowMatrix = mat.toRowMatrix()
rowMat: org.apache.spark.mllib.linalg.distributed.RowMatrix = org.apache.spark.mllib.linalg.distributed.RowMatrix@425fc4a2
rowMat.rows.collect()
res2: Array[org.apache.spark.mllib.linalg.Vector] = Array([1.0,3.0], [4.0,5.0])

IndexedRowMatrix in Python

An IndexedRowMatrix can be created from an RDD of IndexedRows, where IndexedRow is a wrapper over (long, vector). An IndexedRowMatrix can be converted to a RowMatrix by dropping its row indices.

Refer to the IndexedRowMatrix Python docs for more details on the API.

from pyspark.mllib.linalg.distributed import IndexedRow, IndexedRowMatrix

# Create an RDD of indexed rows.
#   - This can be done explicitly with the IndexedRow class:
indexedRows = sc.parallelize([IndexedRow(0, [1, 2, 3]),
                              IndexedRow(1, [4, 5, 6]),
                              IndexedRow(2, [7, 8, 9]),
                              IndexedRow(3, [10, 11, 12])])

#   - or by using (long, vector) tuples:
indexedRows = sc.parallelize([(0, [1, 2, 3]), (1, [4, 5, 6]),
                              (2, [7, 8, 9]), (3, [10, 11, 12])])

# Create an IndexedRowMatrix from an RDD of IndexedRows.
mat = IndexedRowMatrix(indexedRows)

# Get its size.
m = mat.numRows()  # 4
n = mat.numCols()  # 3
print (m,n)

# Get the rows as an RDD of IndexedRows.
rowsRDD = mat.rows

# Convert to a RowMatrix by dropping the row indices.
rowMat = mat.toRowMatrix()

# Convert to a CoordinateMatrix.
coordinateMat = mat.toCoordinateMatrix()

# Convert to a BlockMatrix.
blockMat = mat.toBlockMatrix()
4 3

ScaDaMaLe Course site and book

This is an elaboration of the Apache Spark mllib-progamming-guide on mllib-data-types.

Overview

Data Types - MLlib Programming Guide

MLlib supports local vectors and matrices stored on a single machine, as well as distributed matrices backed by one or more RDDs. Local vectors and local matrices are simple data models that serve as public interfaces. The underlying linear algebra operations are provided by Breeze and jblas. A training example used in supervised learning is called a “labeled point” in MLlib.

CoordinateMatrix in Scala

A CoordinateMatrix is a distributed matrix backed by an RDD of its entries. Each entry is a tuple of (i: Long, j: Long, value: Double), where i is the row index, j is the column index, and value is the entry value. A CoordinateMatrix should be used only when both dimensions of the matrix are huge and the matrix is very sparse.

A CoordinateMatrix can be created from an RDD[MatrixEntry] instance, where MatrixEntry is a wrapper over (Long, Long, Double). A CoordinateMatrix can be converted to an IndexedRowMatrix with sparse rows by calling toIndexedRowMatrix. Other computations for CoordinateMatrix are not currently supported.

Refer to the CoordinateMatrix Scala docs for details on the API.

import org.apache.spark.mllib.linalg.distributed.{CoordinateMatrix, MatrixEntry}
import org.apache.spark.mllib.linalg.distributed.{CoordinateMatrix, MatrixEntry}
val entries: RDD[MatrixEntry] = sc.parallelize(Array(MatrixEntry(0, 0, 1.2), MatrixEntry(1, 0, 2.1), MatrixEntry(6, 1, 3.7))) // an RDD of matrix entries
entries: org.apache.spark.rdd.RDD[org.apache.spark.mllib.linalg.distributed.MatrixEntry] = ParallelCollectionRDD[3712] at parallelize at command-2972105651606627:1
// Create a CoordinateMatrix from an RDD[MatrixEntry].
val mat: CoordinateMatrix = new CoordinateMatrix(entries)
mat: org.apache.spark.mllib.linalg.distributed.CoordinateMatrix = org.apache.spark.mllib.linalg.distributed.CoordinateMatrix@56954954
// Get its size.
val m = mat.numRows()
val n = mat.numCols()
m: Long = 7
n: Long = 2
// Convert it to an IndexRowMatrix whose rows are sparse vectors.
val indexedRowMatrix = mat.toIndexedRowMatrix()
indexedRowMatrix: org.apache.spark.mllib.linalg.distributed.IndexedRowMatrix = org.apache.spark.mllib.linalg.distributed.IndexedRowMatrix@45570b82
indexedRowMatrix.rows.collect()
res0: Array[org.apache.spark.mllib.linalg.distributed.IndexedRow] = Array(IndexedRow(0,(2,[0],[1.2])), IndexedRow(1,(2,[0],[2.1])), IndexedRow(6,(2,[1],[3.7])))

CoordinateMatrix in Scala

A CoordinateMatrix can be created from an RDD of MatrixEntry entries, where MatrixEntry is a wrapper over (long, long, float). A CoordinateMatrix can be converted to a RowMatrix by calling toRowMatrix, or to an IndexedRowMatrix with sparse rows by calling toIndexedRowMatrix.

Refer to the CoordinateMatrix Python docs for more details on the API.

from pyspark.mllib.linalg.distributed import CoordinateMatrix, MatrixEntry

# Create an RDD of coordinate entries.
#   - This can be done explicitly with the MatrixEntry class:
entries = sc.parallelize([MatrixEntry(0, 0, 1.2), MatrixEntry(1, 0, 2.1), MatrixEntry(6, 1, 3.7)])

#   - or using (long, long, float) tuples:
entries = sc.parallelize([(0, 0, 1.2), (1, 0, 2.1), (2, 1, 3.7)])

# Create an CoordinateMatrix from an RDD of MatrixEntries.
mat = CoordinateMatrix(entries)

# Get its size.
m = mat.numRows()  # 3
n = mat.numCols()  # 2
print (m,n)

# Get the entries as an RDD of MatrixEntries.
entriesRDD = mat.entries

# Convert to a RowMatrix.
rowMat = mat.toRowMatrix()

# Convert to an IndexedRowMatrix.
indexedRowMat = mat.toIndexedRowMatrix()

# Convert to a BlockMatrix.
blockMat = mat.toBlockMatrix()
3 2

ScaDaMaLe Course site and book

This is an elaboration of the Apache Spark mllib-progamming-guide on mllib-data-types.

Overview

Data Types - MLlib Programming Guide

MLlib supports local vectors and matrices stored on a single machine, as well as distributed matrices backed by one or more RDDs. Local vectors and local matrices are simple data models that serve as public interfaces. The underlying linear algebra operations are provided by Breeze and jblas. A training example used in supervised learning is called a “labeled point” in MLlib.

BlockMatrix in Scala

A BlockMatrix is a distributed matrix backed by an RDD of MatrixBlocks, where a MatrixBlock is a tuple of ((Int, Int), Matrix), where the (Int, Int) is the index of the block, and Matrix is the sub-matrix at the given index with size rowsPerBlock x colsPerBlock. BlockMatrix supports methods such as add and multiply with another BlockMatrix. BlockMatrix also has a helper function validate which can be used to check whether the BlockMatrix is set up properly.

A BlockMatrix can be most easily created from an IndexedRowMatrix or CoordinateMatrix by calling toBlockMatrix. toBlockMatrix creates blocks of size 1024 x 1024 by default. Users may change the block size by supplying the values through toBlockMatrix(rowsPerBlock, colsPerBlock).

Refer to the BlockMatrix Scala docs for details on the API.

//import org.apache.spark.mllib.linalg.{Matrix, Matrices}
import org.apache.spark.mllib.linalg.distributed.{BlockMatrix, CoordinateMatrix, MatrixEntry}
import org.apache.spark.mllib.linalg.distributed.{BlockMatrix, CoordinateMatrix, MatrixEntry}
val entries: RDD[MatrixEntry] = sc.parallelize(Array(MatrixEntry(0, 0, 1.2), MatrixEntry(1, 0, 2.1), MatrixEntry(6, 1, 3.7))) // an RDD of matrix entries
entries: org.apache.spark.rdd.RDD[org.apache.spark.mllib.linalg.distributed.MatrixEntry] = ParallelCollectionRDD[3746] at parallelize at command-2972105651607062:1
// Create a CoordinateMatrix from an RDD[MatrixEntry].
val coordMat: CoordinateMatrix = new CoordinateMatrix(entries)
coordMat: org.apache.spark.mllib.linalg.distributed.CoordinateMatrix = org.apache.spark.mllib.linalg.distributed.CoordinateMatrix@161a1942
// Transform the CoordinateMatrix to a BlockMatrix
val matA: BlockMatrix = coordMat.toBlockMatrix().cache()
matA: org.apache.spark.mllib.linalg.distributed.BlockMatrix = org.apache.spark.mllib.linalg.distributed.BlockMatrix@1ddf85ce
// Validate whether the BlockMatrix is set up properly. Throws an Exception when it is not valid.
// Nothing happens if it is valid.
matA.validate()
// Calculate A^T A.
val ata = matA.transpose.multiply(matA)
ata: org.apache.spark.mllib.linalg.distributed.BlockMatrix = org.apache.spark.mllib.linalg.distributed.BlockMatrix@18c0eeca
ata.blocks.collect()
res1: Array[((Int, Int), org.apache.spark.mllib.linalg.Matrix)] =
Array(((0,0),5.85  0.0
0.0   13.690000000000001  ))
ata.toLocalMatrix()
res2: org.apache.spark.mllib.linalg.Matrix =
5.85  0.0
0.0   13.690000000000001

BlockMatrix in Scala

A BlockMatrix can be created from an RDD of sub-matrix blocks, where a sub-matrix block is a ((blockRowIndex, blockColIndex), sub-matrix) tuple.

Refer to the BlockMatrix Python docs for more details on the API.

from pyspark.mllib.linalg import Matrices
from pyspark.mllib.linalg.distributed import BlockMatrix

# Create an RDD of sub-matrix blocks.
blocks = sc.parallelize([((0, 0), Matrices.dense(3, 2, [1, 2, 3, 4, 5, 6])),
                         ((1, 0), Matrices.dense(3, 2, [7, 8, 9, 10, 11, 12]))])

# Create a BlockMatrix from an RDD of sub-matrix blocks.
mat = BlockMatrix(blocks, 3, 2)

# Get its size.
m = mat.numRows() # 6
n = mat.numCols() # 2
print (m,n)

# Get the blocks as an RDD of sub-matrix blocks.
blocksRDD = mat.blocks

# Convert to a LocalMatrix.
localMat = mat.toLocalMatrix()

# Convert to an IndexedRowMatrix.
indexedRowMat = mat.toIndexedRowMatrix()

# Convert to a CoordinateMatrix.
coordinateMat = mat.toCoordinateMatrix()
6 2

ScaDaMaLe Course site and book

Power Plant ML Pipeline Application

This is an end-to-end example of using a number of different machine learning algorithms to solve a supervised regression problem.

Table of Contents

  • Step 1: Business Understanding
  • Step 2: Load Your Data
  • Step 3: Explore Your Data
  • Step 4: Visualize Your Data
  • Step 5: Data Preparation
  • Step 6: Data Modeling
  • Step 7: Tuning and Evaluation
  • Step 8: Deployment

We are trying to predict power output given a set of readings from various sensors in a gas-fired power generation plant. Power generation is a complex process, and understanding and predicting power output is an important element in managing a plant and its connection to the power grid.

More information about Peaker or Peaking Power Plants can be found on Wikipedia https://en.wikipedia.org/wiki/Peakingpowerplant

Given this business problem, we need to translate it to a Machine Learning task. The ML task is regression since the label (or target) we are trying to predict is numeric.

The example data is provided by UCI at UCI Machine Learning Repository Combined Cycle Power Plant Data Set

You can read the background on the UCI page, but in summary we have collected a number of readings from sensors at a Gas Fired Power Plant

(also called a Peaker Plant) and now we want to use those sensor readings to predict how much power the plant will generate.

More information about Machine Learning with Spark can be found in the Spark MLLib Programming Guide

Please note this example only works with Spark version 1.4 or higher



To Rerun Steps 1-4 done in the notebook at:

  • Workspace -> PATH_TO -> 009_PowerPlantPipeline_01ETLEDA]

just run the following command as shown in the cell below:

%run "/PATH_TO/009_PowerPlantPipeline_01ETLEDA"
  • Note: If you already evaluated the %run ... command above then:

    • first delete the cell by pressing on x on the top-right corner of the cell and
    • revaluate the run command above.
"../009_PowerPlantPipeline_01ETLEDA" 


Now we will do the following Steps:

Step 5: Data Preparation,

Step 6: Modeling, and

Step 7: Tuning and Evaluation

We will do Step 8: Deployment later after we get introduced to SparkStreaming.

Step 5: Data Preparation

The next step is to prepare the data. Since all of this data is numeric and consistent, this is a simple task for us today.

We will need to convert the predictor features from columns to Feature Vectors using the org.apache.spark.ml.feature.VectorAssembler

The VectorAssembler will be the first step in building our ML pipeline.

res2: Int = 301
//Let's quickly recall the schema and make sure our table is here now
table("power_plant_table").printSchema
root
 |-- AT: double (nullable = true)
 |-- V: double (nullable = true)
 |-- AP: double (nullable = true)
 |-- RH: double (nullable = true)
 |-- PE: double (nullable = true)
path name size
dbfs:/databricks-datasets/power-plant/data/Sheet1.tsv Sheet1.tsv 308693.0
dbfs:/databricks-datasets/power-plant/data/Sheet2.tsv Sheet2.tsv 308693.0
dbfs:/databricks-datasets/power-plant/data/Sheet3.tsv Sheet3.tsv 308693.0
dbfs:/databricks-datasets/power-plant/data/Sheet4.tsv Sheet4.tsv 308693.0
dbfs:/databricks-datasets/power-plant/data/Sheet5.tsv Sheet5.tsv 308693.0
powerPlantRDD: org.apache.spark.rdd.RDD[String] = /databricks-datasets/power-plant/data/Sheet1.tsv MapPartitionsRDD[1] at textFile at command-1267216879634554:1
powerPlantDF // make sure we have the DataFrame too
res82: org.apache.spark.sql.DataFrame = [AT: double, V: double ... 3 more fields]
AT	V	AP	RH	PE
14.96	41.76	1024.07	73.17	463.26
25.18	62.96	1020.04	59.08	444.37
5.11	39.4	1012.16	92.14	488.56
20.86	57.32	1010.24	76.64	446.48
powerPlantDF: org.apache.spark.sql.DataFrame = [AT: double, V: double ... 3 more fields]
root
 |-- AT: double (nullable = true)
 |-- V: double (nullable = true)
 |-- AP: double (nullable = true)
 |-- RH: double (nullable = true)
 |-- PE: double (nullable = true)
import org.apache.spark.ml.feature.VectorAssembler

// make a DataFrame called dataset from the table
val dataset = sqlContext.table("power_plant_table") 

val vectorizer =  new VectorAssembler()
                      .setInputCols(Array("AT", "V", "AP", "RH"))
                      .setOutputCol("features")
import org.apache.spark.ml.feature.VectorAssembler
dataset: org.apache.spark.sql.DataFrame = [AT: double, V: double ... 3 more fields]
vectorizer: org.apache.spark.ml.feature.VectorAssembler = VectorAssembler: uid=vecAssembler_ea4ed428c7e4, handleInvalid=error, numInputCols=4
res9: Long = 9568
+-----+-----+-------+-----+------+
|   AT|    V|     AP|   RH|    PE|
+-----+-----+-------+-----+------+
|14.96|41.76|1024.07|73.17|463.26|
|25.18|62.96|1020.04|59.08|444.37|
| 5.11| 39.4|1012.16|92.14|488.56|
|20.86|57.32|1010.24|76.64|446.48|
|10.82| 37.5|1009.23|96.62| 473.9|
|26.27|59.44|1012.23|58.77|443.67|
|15.89|43.96|1014.02|75.24|467.35|
| 9.48|44.71|1019.12|66.43|478.42|
|14.64| 45.0|1021.78|41.25|475.98|
|11.74|43.56|1015.14|70.72| 477.5|
+-----+-----+-------+-----+------+
only showing top 10 rows
AT V AP RH PE
14.96 41.76 1024.07 73.17 463.26
25.18 62.96 1020.04 59.08 444.37
5.11 39.4 1012.16 92.14 488.56
20.86 57.32 1010.24 76.64 446.48
10.82 37.5 1009.23 96.62 473.9
26.27 59.44 1012.23 58.77 443.67
15.89 43.96 1014.02 75.24 467.35
9.48 44.71 1019.12 66.43 478.42
14.64 45.0 1021.78 41.25 475.98
11.74 43.56 1015.14 70.72 477.5
17.99 43.72 1008.64 75.04 453.02
20.14 46.93 1014.66 64.22 453.99
24.34 73.5 1011.31 84.15 440.29
25.71 58.59 1012.77 61.83 451.28
26.19 69.34 1009.48 87.59 433.99
21.42 43.79 1015.76 43.08 462.19
18.21 45.0 1022.86 48.84 467.54
11.04 41.74 1022.6 77.51 477.2
14.45 52.75 1023.97 63.59 459.85
13.97 38.47 1015.15 55.28 464.3
17.76 42.42 1009.09 66.26 468.27
5.41 40.07 1019.16 64.77 495.24
7.76 42.28 1008.52 83.31 483.8
27.23 63.9 1014.3 47.19 443.61
27.36 48.6 1003.18 54.93 436.06
27.47 70.72 1009.97 74.62 443.25
14.6 39.31 1011.11 72.52 464.16
7.91 39.96 1023.57 88.44 475.52
5.81 35.79 1012.14 92.28 484.41
30.53 65.18 1012.69 41.85 437.89
23.87 63.94 1019.02 44.28 445.11
26.09 58.41 1013.64 64.58 438.86
29.27 66.85 1011.11 63.25 440.98
27.38 74.16 1010.08 78.61 436.65
24.81 63.94 1018.76 44.51 444.26
12.75 44.03 1007.29 89.46 465.86
24.66 63.73 1011.4 74.52 444.37
16.38 47.45 1010.08 88.86 450.69
13.91 39.35 1014.69 75.51 469.02
23.18 51.3 1012.04 78.64 448.86
22.47 47.45 1007.62 76.65 447.14
13.39 44.85 1017.24 80.44 469.18
9.28 41.54 1018.33 79.89 482.8
11.82 42.86 1014.12 88.28 476.7
10.27 40.64 1020.63 84.6 474.99
22.92 63.94 1019.28 42.69 444.22
16.0 37.87 1020.24 78.41 461.33
21.22 43.43 1010.96 61.07 448.06
13.46 44.71 1014.51 50.0 474.6
9.39 40.11 1029.14 77.29 473.05
31.07 73.5 1010.58 43.66 432.06
12.82 38.62 1018.71 83.8 467.41
32.57 78.92 1011.6 66.47 430.12
8.11 42.18 1014.82 93.09 473.62
13.92 39.39 1012.94 80.52 471.81
23.04 59.43 1010.23 68.99 442.99
27.31 64.44 1014.65 57.27 442.77
5.91 39.33 1010.18 95.53 491.49
25.26 61.08 1013.68 71.72 447.46
27.97 58.84 1002.25 57.88 446.11
26.08 52.3 1007.03 63.34 442.44
29.01 65.71 1013.61 48.07 446.22
12.18 40.1 1016.67 91.87 471.49
13.76 45.87 1008.89 87.27 463.5
25.5 58.79 1016.02 64.4 440.01
28.26 65.34 1014.56 43.4 441.03
21.39 62.96 1019.49 72.24 452.68
7.26 40.69 1020.43 90.22 474.91
10.54 34.03 1018.71 74.0 478.77
27.71 74.34 998.14 71.85 434.2
23.11 68.3 1017.83 86.62 437.91
7.51 41.01 1024.61 97.41 477.61
26.46 74.67 1016.65 84.44 431.65
29.34 74.34 998.58 81.55 430.57
10.32 42.28 1008.82 75.66 481.09
22.74 61.02 1009.56 79.41 445.56
13.48 39.85 1012.71 58.91 475.74
25.52 69.75 1010.36 90.06 435.12
21.58 67.25 1017.39 79.0 446.15
27.66 76.86 1001.31 69.47 436.64
26.96 69.45 1013.89 51.47 436.69
12.29 42.18 1016.53 83.13 468.75
15.86 43.02 1012.18 40.33 466.6
13.87 45.08 1024.42 81.69 465.48
24.09 73.68 1014.93 94.55 441.34
20.45 69.45 1012.53 91.81 441.83
15.07 39.3 1019.0 63.62 464.7
32.72 69.75 1009.6 49.35 437.99
18.23 58.96 1015.55 69.61 459.12
35.56 68.94 1006.56 38.75 429.69
18.36 51.43 1010.57 90.17 459.8
26.35 64.05 1009.81 81.24 433.63
25.92 60.95 1014.62 48.46 442.84
8.01 41.66 1014.49 76.72 485.13
19.63 52.72 1025.09 51.16 459.12
20.02 67.32 1012.05 76.34 445.31
10.08 40.72 1022.7 67.3 480.8
27.23 66.48 1005.23 52.38 432.55
23.37 63.77 1013.42 76.44 443.86
18.74 59.21 1018.3 91.55 449.77
14.81 43.69 1017.19 71.9 470.71
23.1 51.3 1011.93 80.05 452.17
10.72 41.38 1021.6 63.77 478.29
29.46 71.94 1006.96 62.26 428.54
8.1 40.64 1020.66 89.04 478.27
27.29 62.66 1007.63 58.02 439.58
17.1 49.69 1005.53 81.82 457.32
11.49 44.2 1018.79 91.14 475.51
23.69 65.59 1010.85 88.92 439.66
13.51 40.89 1011.03 84.83 471.99
9.64 39.35 1015.1 91.76 479.81
25.65 78.92 1010.83 86.56 434.78
21.59 61.87 1011.18 57.21 446.58
27.98 58.33 1013.92 54.25 437.76
18.8 39.72 1001.24 63.8 459.36
18.28 44.71 1016.99 33.71 462.28
13.55 43.48 1016.08 67.25 464.33
22.99 46.21 1010.71 60.11 444.36
23.94 59.39 1014.32 74.55 438.64
13.74 34.03 1018.69 67.34 470.49
21.3 41.1 1001.86 42.75 455.13
27.54 66.93 1017.06 55.2 450.22
24.81 63.73 1009.34 83.61 440.43
4.97 42.85 1014.02 88.78 482.98
15.22 50.88 1014.19 100.12 460.44
23.88 54.2 1012.81 64.52 444.97
33.01 68.67 1005.2 51.41 433.94
25.98 73.18 1012.28 85.78 439.73
28.18 73.88 1005.89 75.41 434.48
21.67 60.84 1017.93 81.63 442.33
17.67 45.09 1014.26 51.92 457.67
21.37 57.76 1018.8 70.12 454.66
28.69 67.25 1017.71 53.83 432.21
16.61 43.77 1012.25 77.23 457.66
27.91 63.76 1010.27 65.67 435.21
20.97 47.43 1007.64 71.18 448.22
10.8 41.66 1013.79 81.96 475.51
20.61 62.91 1013.24 79.54 446.53
25.45 57.32 1011.7 47.09 441.3
30.16 69.34 1007.67 57.69 433.54
4.99 39.04 1020.45 78.89 472.52
10.51 44.78 1012.59 85.29 474.77
33.79 69.05 1001.62 40.13 435.1
21.34 59.8 1016.92 77.06 450.74
23.4 65.06 1014.32 67.38 442.7
32.21 68.14 1003.34 62.44 426.56
14.26 42.32 1016.0 77.43 463.71
27.71 66.93 1016.85 58.77 447.06
21.95 57.76 1018.02 67.72 452.27
25.76 63.94 1018.49 42.14 445.78
23.68 68.3 1017.93 84.16 438.65
8.28 40.77 1011.55 89.79 480.15
23.44 62.52 1016.46 67.21 447.19
25.32 48.41 1008.47 72.14 443.04
3.94 39.9 1008.06 97.49 488.81
17.3 57.76 1016.26 87.74 455.75
18.2 49.39 1018.83 96.3 455.86
21.43 46.97 1013.94 61.25 457.68
11.16 40.05 1014.95 88.38 479.11
30.38 74.16 1007.44 74.77 432.84
23.36 62.52 1016.18 68.18 448.37
21.69 47.45 1007.56 77.2 447.06
23.62 49.21 1014.1 49.54 443.53
21.87 61.45 1011.13 92.22 445.21
29.25 66.51 1015.53 33.65 441.7
20.03 66.86 1013.05 64.59 450.93
18.14 49.78 1002.95 100.09 451.44
24.23 56.89 1012.32 68.04 441.29
18.11 44.85 1014.48 48.94 458.85
6.57 43.65 1018.24 74.47 481.46
12.56 43.41 1016.93 81.02 467.19
13.4 41.58 1020.5 71.17 461.54
27.1 52.84 1006.28 53.85 439.08
14.28 42.74 1028.79 70.67 467.22
16.29 44.34 1019.49 59.36 468.8
31.24 71.98 1004.66 57.17 426.93
10.57 37.73 1024.36 70.29 474.65
13.8 44.21 1022.93 83.37 468.97
25.3 71.58 1010.18 87.36 433.97
18.06 50.16 1009.52 100.09 450.53
25.42 59.04 1011.98 68.78 444.51
15.07 40.69 1015.29 70.98 469.03
11.75 71.14 1019.36 75.68 466.56
20.23 52.05 1012.15 47.49 457.57
27.31 59.54 1006.24 71.99 440.13
28.57 69.84 1003.57 66.55 433.24
17.9 43.72 1008.64 74.73 452.55
23.83 71.37 1002.04 64.78 443.29
27.92 74.99 1005.47 75.13 431.76
17.34 44.78 1007.81 56.38 454.97
17.94 63.07 1012.42 94.35 456.7
6.4 39.9 1007.75 86.55 486.03
11.78 39.96 1011.37 82.95 472.79
20.28 57.25 1010.12 88.42 452.03
21.04 54.2 1012.26 85.61 443.41
25.11 67.32 1014.49 58.39 441.93
30.28 70.98 1007.51 74.28 432.64
8.14 36.24 1013.15 87.85 480.25
16.86 39.63 1004.47 83.5 466.68
6.25 40.07 1020.19 65.24 494.39
22.35 54.42 1012.46 75.01 454.72
17.98 56.85 1012.28 84.52 448.71
21.19 42.48 1013.43 80.52 469.76
20.94 44.89 1009.64 75.14 450.71
24.23 58.79 1009.8 75.75 444.01
19.18 58.2 1017.46 76.72 453.2
20.88 57.85 1012.39 85.47 450.87
23.67 63.86 1019.67 57.95 441.73
14.12 39.52 1018.41 78.32 465.09
25.23 64.63 1020.59 52.2 447.28
6.54 39.33 1011.54 93.69 491.16
20.08 62.52 1017.99 75.74 450.98
24.67 63.56 1013.75 67.56 446.3
27.82 79.74 1008.37 69.46 436.48
15.55 42.03 1017.41 74.58 460.84
24.26 69.51 1013.43 53.23 442.56
13.45 41.49 1020.19 88.72 467.3
11.06 40.64 1021.47 96.16 479.13
24.91 52.3 1008.72 68.26 441.15
22.39 59.04 1011.78 86.39 445.52
11.95 40.69 1015.62 85.34 475.4
14.85 40.69 1014.91 72.64 469.3
10.11 41.62 1017.17 97.82 463.57
23.67 68.67 1006.71 77.22 445.32
16.14 44.21 1020.36 80.59 461.03
15.11 43.13 1014.99 46.91 466.74
24.14 59.87 1018.47 57.76 444.04
30.08 67.25 1017.6 53.09 434.01
14.77 44.9 1020.5 84.31 465.23
27.6 69.34 1009.63 71.58 440.6
13.89 44.84 1023.66 92.97 466.74
26.85 75.6 1017.43 74.55 433.48
12.41 40.96 1023.36 78.96 473.59
13.08 41.74 1020.75 64.44 474.81
18.93 44.06 1017.58 68.23 454.75
20.5 49.69 1009.6 70.81 452.94
30.72 69.13 1009.94 61.66 435.83
7.55 39.22 1014.53 77.76 482.19
13.49 44.47 1030.46 69.49 466.66
15.62 40.12 1013.03 96.26 462.59
24.8 64.63 1020.69 55.74 447.82
10.03 41.62 1014.55 95.61 462.73
22.43 63.21 1012.06 84.75 447.98
14.95 39.31 1009.15 75.3 462.72
24.78 58.46 1016.82 67.5 442.42
23.2 48.41 1008.64 80.92 444.69
14.01 39.0 1016.73 79.23 466.7
19.4 64.63 1020.38 81.1 453.84
30.15 67.32 1013.83 32.8 436.92
6.91 36.08 1021.82 84.31 486.37
29.04 60.07 1015.42 46.15 440.43
26.02 63.07 1010.94 53.96 446.82
5.89 39.48 1005.11 59.83 484.91
26.52 71.64 1008.27 75.3 437.76
28.53 68.08 1013.27 42.53 438.91
16.59 39.54 1007.97 70.58 464.19
22.95 67.79 1009.89 91.69 442.19
23.96 47.43 1008.38 63.55 446.86
17.48 44.2 1018.89 61.51 457.15
6.69 43.65 1020.14 69.55 482.57
10.25 41.26 1007.44 98.08 476.03
28.87 72.58 1008.69 79.34 428.89
12.04 40.23 1018.07 81.28 472.7
22.58 52.3 1009.04 78.99 445.6
15.12 52.05 1014.63 80.38 464.78
25.48 58.95 1017.02 51.16 440.42
27.87 70.79 1003.96 72.17 428.41
23.72 70.47 1010.65 75.39 438.5
25.0 59.43 1007.84 68.91 438.28
8.42 40.64 1022.35 96.38 476.29
22.46 58.49 1011.5 70.54 448.46
29.92 57.19 1008.62 45.8 438.99
11.68 39.22 1017.9 57.95 471.8
14.04 42.44 1012.74 81.89 471.81
19.86 59.14 1016.12 69.32 449.82
25.99 68.08 1013.13 59.14 442.14
23.42 58.79 1009.74 81.54 441.46
10.6 40.22 1011.37 85.81 477.62
20.97 61.87 1011.45 65.41 446.76
14.14 39.82 1012.46 81.15 472.52
8.56 40.71 1021.27 95.87 471.58
24.86 72.39 1001.15 90.24 440.85
29.0 77.54 1011.33 75.13 431.37
27.59 71.97 1008.64 88.22 437.33
10.45 40.71 1015.68 81.48 469.22
8.51 40.78 1023.51 89.84 471.11
29.82 66.51 1010.98 43.57 439.17
22.56 62.26 1012.11 63.16 445.33
11.38 39.22 1018.62 57.14 473.71
20.25 57.76 1016.28 77.76 452.66
22.42 59.43 1007.12 90.56 440.99
14.85 38.91 1014.48 60.98 467.42
25.62 58.82 1010.02 70.31 444.14
19.85 56.53 1020.57 74.05 457.17
13.67 54.3 1015.92 75.42 467.87
24.39 70.72 1009.78 82.25 442.04
16.07 44.58 1019.52 67.95 471.36
11.6 39.1 1009.81 100.09 460.7
31.38 70.83 1010.35 47.28 431.33
29.91 76.86 998.59 72.41 432.6
19.67 59.39 1014.07 77.67 447.61
27.18 64.79 1016.27 63.7 443.87
21.39 52.3 1009.2 79.77 446.87
10.45 41.01 1020.57 93.84 465.74
19.46 56.89 1014.02 84.95 447.86
23.55 62.96 1020.16 70.16 447.65
23.35 63.47 1011.78 84.24 437.87
9.26 41.66 1016.87 73.32 483.51
10.3 41.46 1018.21 86.17 479.65
20.94 58.16 1016.88 65.43 455.16
23.13 71.25 1002.49 94.59 431.91
12.77 41.5 1014.13 86.8 470.68
28.29 69.13 1009.29 58.18 429.28
19.13 59.21 1018.32 89.66 450.81
24.44 73.5 1011.49 87.39 437.73
20.32 44.6 1015.16 36.35 460.21
20.54 69.05 1001.6 79.62 442.86
12.16 45.0 1021.51 50.52 482.99
28.09 65.27 1013.27 51.96 440.0
9.25 41.82 1033.25 74.73 478.48
21.75 49.82 1015.01 78.33 455.28
23.7 66.56 1002.07 85.19 436.94
16.22 37.87 1022.36 83.13 461.06
24.75 69.45 1013.97 53.49 438.28
10.48 39.58 1011.81 88.86 472.61
29.53 70.79 1003.7 60.89 426.85
12.59 39.72 1017.76 61.14 470.18
23.5 54.42 1012.31 68.29 455.38
29.01 66.56 1006.44 57.62 428.32
9.75 42.49 1010.57 83.63 480.35
19.55 56.53 1020.2 78.1 455.56
21.05 58.33 1013.14 66.34 447.66
24.72 68.67 1006.74 79.02 443.06
21.19 58.86 1014.19 68.96 452.43
10.77 41.54 1019.94 71.13 477.81
28.68 73.77 1004.72 87.01 431.66
29.87 73.91 1004.53 74.3 431.8
22.99 68.67 1006.65 77.62 446.67
24.66 60.29 1018.0 59.56 445.26
32.63 69.89 1013.85 41.66 425.72
31.38 72.29 1008.73 73.27 430.58
23.87 60.27 1018.94 77.16 439.86
25.6 59.15 1013.31 67.02 441.11
27.62 71.14 1011.6 52.8 434.72
30.1 67.45 1014.23 39.04 434.01
12.19 41.17 1019.43 65.47 475.64
13.11 41.58 1020.43 74.32 460.44
28.29 68.67 1005.46 69.22 436.4
13.45 40.73 1018.7 93.88 461.03
10.98 41.54 1019.94 69.83 479.08
26.48 69.14 1009.31 84.11 435.76
13.07 45.51 1015.22 78.65 460.14
25.56 75.6 1017.37 69.31 442.2
22.68 50.78 1008.83 70.3 447.69
28.86 73.67 1006.65 68.23 431.15
22.7 63.56 1014.32 71.76 445.0
27.89 73.21 1001.32 85.88 431.59
13.78 44.47 1027.94 71.09 467.22
28.14 51.43 1012.16 52.67 445.33
11.8 45.09 1013.21 89.68 470.57
10.71 39.61 1018.72 73.66 473.77
24.54 60.29 1017.42 58.94 447.67
11.54 40.05 1014.78 87.05 474.29
29.47 71.32 1008.07 67.0 437.14
29.24 69.05 1003.12 43.18 432.56
14.51 41.79 1009.72 80.62 459.14
22.91 60.07 1016.03 59.72 446.19
27.02 71.77 1006.38 72.1 428.1
13.49 44.47 1030.18 69.15 468.46
30.24 66.75 1017.95 55.66 435.02
23.19 48.6 1002.38 61.19 445.52
17.73 40.55 1003.36 74.62 462.69
18.62 61.27 1019.26 73.35 455.75
12.85 40.0 1015.89 68.85 463.74
32.33 69.68 1011.95 39.89 439.79
25.09 58.95 1016.99 53.16 443.26
29.45 69.13 1009.3 52.97 432.04
16.91 43.96 1013.32 79.87 465.86
14.09 45.87 1009.05 84.09 465.6
10.73 25.36 1009.35 100.15 469.43
23.2 49.3 1003.4 79.77 440.75
8.21 38.91 1015.82 88.99 481.32
9.3 40.56 1022.64 76.14 479.87
16.97 39.16 1005.7 69.13 458.59
23.69 71.97 1009.62 93.03 438.62
25.13 59.44 1012.38 77.92 445.59
9.86 43.56 1015.13 74.89 481.87
11.33 41.5 1013.58 88.7 475.01
26.95 48.41 1008.53 62.94 436.54
15.0 40.66 1016.28 89.62 456.63
20.76 62.52 1015.63 81.04 451.69
14.29 39.59 1010.93 94.53 463.04
19.74 67.71 1007.68 64.02 446.1
26.68 59.92 1009.94 70.57 438.67
14.24 41.4 1019.7 70.32 466.88
21.98 48.41 1008.42 84.86 444.6
22.75 59.39 1015.4 81.41 440.26
8.34 40.96 1023.28 89.45 483.92
11.8 41.2 1017.18 82.71 475.19
8.81 44.68 1023.06 93.93 479.24
30.05 73.68 1014.95 70.6 434.92
16.01 65.46 1014.0 87.68 454.16
21.75 58.79 1012.42 87.58 447.58
13.94 41.26 1021.67 74.4 467.9
29.25 69.13 1010.27 67.35 426.29
22.33 45.87 1007.8 63.61 447.02
16.43 41.79 1005.47 76.89 455.85
11.5 40.22 1010.31 78.08 476.46
23.53 68.94 1007.53 69.17 437.48
21.86 49.21 1014.61 53.31 452.77
6.17 39.33 1012.57 93.32 491.54
30.19 64.79 1017.22 42.47 438.41
11.67 41.93 1019.81 82.58 476.1
15.34 36.99 1007.87 94.59 464.58
11.5 40.78 1023.91 86.31 467.74
25.53 57.17 1010.0 72.57 442.12
21.27 57.5 1014.53 80.76 453.34
28.37 69.13 1010.44 71.93 425.29
28.39 51.43 1011.74 47.54 449.63
13.78 45.78 1025.27 95.72 462.88
14.6 42.32 1015.71 77.03 464.67
5.1 35.57 1027.17 80.49 489.96
7.0 38.08 1020.27 77.67 482.38
26.3 77.95 1009.45 78.72 437.95
30.56 71.98 1004.74 58.77 429.2
21.09 46.63 1013.03 74.8 453.34
28.21 70.02 1010.58 51.34 442.47
15.84 49.69 1015.14 90.41 462.6
10.03 40.96 1024.57 91.1 478.79
20.37 52.05 1012.34 62.57 456.11
21.19 50.16 1005.81 84.27 450.33
33.73 69.88 1007.21 42.93 434.83
29.87 73.68 1015.1 40.96 433.43
19.62 62.96 1020.76 76.53 456.02
9.93 40.67 1018.08 69.74 485.23
9.43 37.14 1013.03 74.99 473.57
14.24 39.58 1011.17 70.45 469.94
12.97 49.83 1008.69 91.49 452.07
7.6 41.04 1021.82 88.97 475.32
8.39 36.24 1013.39 89.13 480.69
25.41 48.06 1013.12 46.52 444.01
18.43 56.03 1020.41 60.55 465.17
10.31 39.82 1012.87 88.71 480.61
11.29 41.5 1013.39 89.15 476.04
22.61 49.3 1003.51 83.02 441.76
29.34 71.98 1005.19 75.19 428.24
18.87 67.71 1004.0 87.35 444.77
13.21 45.87 1008.58 85.66 463.1
11.3 44.6 1018.19 91.66 470.5
29.23 72.99 1007.04 63.47 431.0
27.76 69.4 1004.27 72.25 430.68
29.26 67.17 1006.6 70.58 436.42
25.72 49.82 1016.19 60.1 452.33
23.43 63.94 1010.64 89.29 440.16
25.6 63.76 1010.18 67.43 435.75
22.3 44.57 1008.48 67.58 449.74
27.91 72.24 1010.74 70.8 430.73
30.35 77.17 1009.55 63.62 432.75
21.78 47.43 1007.88 66.68 446.79
7.19 41.39 1018.12 90.76 486.35
20.88 59.8 1015.66 75.34 453.18
24.19 50.23 1015.73 59.77 458.31
9.98 41.54 1019.7 80.79 480.26
23.47 51.3 1011.89 74.1 448.65
26.35 49.5 1012.67 41.34 458.41
29.89 64.69 1006.37 58.78 435.39
19.29 50.16 1010.49 97.78 450.21
17.48 43.14 1018.68 74.85 459.59
25.21 75.6 1017.19 69.84 445.84
23.3 48.78 1018.17 75.36 441.08
15.42 37.85 1009.89 85.8 467.33
21.44 63.09 1016.56 90.11 444.19
29.45 68.27 1007.96 61.63 432.96
29.69 47.93 1002.85 44.76 438.09
15.52 36.99 1006.86 89.7 467.9
11.47 43.67 1012.68 72.51 475.72
9.77 34.69 1027.72 74.98 477.51
22.6 69.84 1006.37 79.59 435.13
8.24 39.61 1017.99 78.42 477.9
17.01 44.2 1019.18 61.23 457.26
19.64 44.6 1015.88 47.56 467.53
10.61 41.58 1021.08 93.06 465.15
12.04 40.1 1014.42 89.65 474.28
29.19 65.71 1013.85 50.5 444.49
21.75 45.09 1014.15 44.84 452.84
23.66 77.54 1008.5 85.32 435.38
27.05 75.33 1003.88 82.94 433.57
29.63 69.71 1009.04 67.26 435.27
18.2 39.63 1005.35 79.05 468.49
32.22 70.8 1009.9 62.03 433.07
26.88 73.56 1004.85 94.36 430.63
29.05 65.74 1013.29 60.02 440.74
8.9 39.96 1026.31 95.46 474.49
18.93 48.6 1005.72 84.92 449.74
27.49 63.76 1010.09 62.8 436.73
23.1 70.79 1006.53 90.81 434.58
11.22 43.13 1017.24 80.9 473.93
31.97 79.74 1007.03 55.84 435.99
13.32 43.22 1009.45 75.3 466.83
31.68 68.24 1005.29 37.34 427.22
23.69 63.77 1013.39 79.5 444.07
13.83 41.49 1020.11 87.29 469.57
18.32 66.51 1015.18 81.5 459.89
11.05 40.71 1024.91 76.42 479.59
22.03 64.69 1007.21 75.75 440.92
10.23 41.46 1020.45 84.95 480.87
23.92 66.54 1009.93 62.37 441.9
29.38 69.68 1011.35 49.25 430.2
17.35 42.86 1014.62 74.16 465.16
9.81 44.45 1021.19 90.55 471.32
4.97 40.64 1020.91 94.28 485.43
5.15 40.07 1012.27 63.31 495.35
21.54 58.49 1010.85 78.9 449.12
7.94 42.02 1006.22 90.97 480.53
18.77 50.66 1014.89 87.34 457.07
21.69 69.94 1010.7 80.8 443.67
10.07 44.68 1023.44 90.95 477.52
13.83 39.64 1012.52 69.97 472.95
10.45 39.69 1003.92 89.45 472.54
11.56 40.71 1015.85 76.08 469.17
23.64 70.04 1011.09 83.35 435.21
10.48 40.22 1004.81 92.16 477.78
13.09 39.85 1012.86 58.42 475.89
10.67 40.23 1017.75 85.06 483.9
12.57 39.16 1016.53 88.91 476.2
14.45 43.34 1015.47 83.33 462.16
14.22 37.85 1011.24 88.49 471.05
6.97 41.26 1010.6 96.88 484.71
20.61 63.86 1015.43 73.86 446.34
14.67 42.28 1007.21 65.17 469.02
29.06 72.86 1004.23 69.41 432.12
14.38 40.1 1015.51 81.23 467.28
32.51 69.98 1013.29 54.07 429.66
11.79 45.09 1013.16 89.17 469.49
8.65 40.56 1023.23 78.85 485.87
9.75 40.81 1026.0 84.44 481.95
9.11 40.02 1031.1 83.02 479.03
23.39 69.13 1010.99 90.66 434.5
14.3 54.3 1015.16 75.29 464.9
17.49 63.94 1020.02 82.6 452.71
31.1 69.51 1010.84 45.4 429.74
19.77 56.65 1020.67 66.33 457.09
28.61 72.29 1011.61 45.33 446.77
13.52 41.48 1014.46 67.12 460.76
13.52 40.83 1008.31 84.14 471.95
17.57 46.21 1014.09 80.81 453.29
28.18 60.07 1016.34 49.13 441.61
14.29 46.18 1017.01 87.29 464.73
18.12 43.69 1016.91 52.95 464.68
31.27 73.91 1003.72 68.92 430.59
26.24 77.95 1014.19 85.21 438.01
7.44 41.04 1021.84 88.56 479.08
29.78 74.78 1009.28 55.09 436.39
23.37 65.46 1016.25 48.64 447.07
10.62 39.58 1011.9 87.85 479.91
5.84 43.02 1013.88 87.42 489.05
14.51 53.82 1016.46 62.75 463.17
11.31 42.02 1001.18 94.86 471.26
11.25 40.67 1011.64 63.54 480.49
9.18 39.42 1025.41 69.46 473.78
19.82 58.16 1016.76 74.66 455.5
24.77 58.41 1013.78 80.57 446.27
9.66 41.06 1021.21 84.7 482.2
21.96 59.8 1016.72 72.6 452.48
18.59 43.14 1011.92 52.63 464.48
24.75 69.89 1015.29 82.01 438.1
24.37 63.47 1012.77 75.22 445.6
29.6 67.79 1010.37 51.05 442.43
25.32 61.25 1011.56 80.1 436.67
16.15 41.85 1016.54 81.58 466.56
15.74 71.14 1019.65 65.94 457.29
5.97 36.25 1029.65 86.74 487.03
15.84 52.72 1026.45 62.57 464.93
14.84 44.63 1019.28 57.37 466.0
12.25 48.79 1017.44 88.91 469.52
27.38 70.04 1011.18 72.26 428.88
8.76 41.48 1018.49 74.98 474.3
15.54 39.31 1009.69 71.19 461.06
18.71 39.39 1014.09 62.82 465.57
13.06 41.78 1012.3 55.31 467.67
12.72 40.71 1016.02 71.57 466.99
19.83 39.39 1013.73 59.16 463.72
27.23 49.16 1004.03 40.8 443.78
24.27 68.28 1005.43 67.63 445.23
11.8 40.66 1017.13 97.2 464.43
6.76 36.25 1028.31 91.16 484.36
25.99 63.07 1012.5 64.81 442.16
16.3 39.63 1004.64 85.61 464.11
16.5 49.39 1018.35 93.42 462.48
10.59 42.49 1009.59 77.36 477.49
26.05 65.59 1012.78 67.03 437.04
19.5 40.79 1003.8 89.45 457.09
22.21 45.01 1012.22 54.84 450.6
17.86 45.0 1023.25 53.48 465.78
29.96 70.04 1010.15 54.47 427.1
19.08 44.63 1020.14 43.36 459.81
23.59 47.43 1006.64 48.92 447.36
3.38 39.64 1011.0 81.22 488.92
26.39 66.49 1012.96 60.35 433.36
8.99 39.04 1021.99 75.98 483.35
10.91 41.04 1026.57 74.24 469.53
13.08 39.82 1012.27 85.21 476.96
23.95 58.46 1017.5 68.46 440.75
15.64 43.71 1024.51 78.31 462.55
18.78 54.2 1012.05 89.25 448.04
20.65 50.59 1016.22 68.57 455.24
4.96 40.07 1011.8 67.38 494.75
23.51 57.32 1012.55 53.6 444.58
5.99 35.79 1011.56 91.69 484.82
23.65 66.05 1019.6 78.21 442.9
5.17 39.33 1009.68 94.19 485.46
26.38 49.5 1012.82 37.19 457.81
6.02 43.65 1013.85 83.53 481.92
23.2 61.02 1009.63 79.45 443.23
8.57 39.69 1000.91 99.9 474.29
30.72 71.58 1009.98 50.39 430.46
21.52 50.66 1013.56 74.33 455.71
22.93 62.26 1011.25 83.66 438.34
5.71 41.31 1003.24 89.48 485.83
18.62 44.06 1017.76 64.59 452.82
27.88 68.94 1007.68 75.68 435.04
22.32 59.8 1016.82 64.18 451.21
14.55 42.74 1028.41 70.09 465.81
17.83 44.92 1025.04 70.58 458.42
9.68 39.96 1026.09 99.28 470.22
19.41 49.39 1020.84 81.89 449.24
13.22 44.92 1023.84 87.99 471.43
12.24 44.92 1023.74 88.21 473.26
19.21 58.49 1011.7 91.29 452.82
29.74 70.32 1008.1 52.72 432.69
23.28 60.84 1017.91 67.5 444.13
8.02 41.92 1029.8 92.05 467.21
22.47 48.6 1002.33 63.23 445.98
27.51 73.77 1002.42 90.88 436.91
17.51 44.9 1009.05 74.91 455.01
23.22 66.56 1002.47 85.39 437.11
11.73 40.64 1020.68 96.98 477.06
21.19 67.71 1006.65 56.28 441.71
5.48 40.07 1019.63 65.62 495.76
24.26 66.44 1011.33 55.32 445.63
12.32 41.62 1012.88 88.88 464.72
31.26 68.94 1005.94 39.49 438.03
32.09 72.86 1003.47 54.59 434.78
24.98 60.32 1015.63 57.19 444.67
27.48 61.41 1012.2 45.06 452.24
21.04 45.09 1014.19 40.62 450.92
27.75 70.4 1006.65 90.21 436.53
22.79 71.77 1005.75 90.91 435.53
24.22 68.51 1013.23 74.96 440.01
27.06 64.45 1008.72 54.21 443.1
29.25 71.94 1007.18 63.62 427.49
26.86 68.08 1012.99 50.04 436.25
29.64 67.79 1009.99 51.23 440.74
19.92 63.31 1015.02 82.71 443.54
18.5 51.43 1010.82 92.04 459.42
23.71 60.23 1009.76 90.67 439.66
14.39 44.84 1023.55 91.14 464.15
19.3 56.65 1020.55 70.43 459.1
24.65 52.36 1014.76 66.63 455.68
13.5 45.51 1015.33 86.95 469.08
9.82 41.26 1007.71 96.69 478.02
18.4 44.06 1017.36 70.88 456.8
28.12 44.89 1009.18 47.14 441.13
17.15 43.69 1017.05 63.36 463.88
30.69 73.67 1006.14 60.58 430.45
28.82 65.71 1014.24 54.3 449.18
21.3 48.92 1010.92 65.09 447.89
30.58 70.04 1010.4 48.16 431.59
21.17 52.3 1009.36 81.51 447.5
9.87 41.82 1033.04 68.57 475.58
22.18 59.8 1016.77 73.16 453.24
24.39 63.21 1012.59 80.88 446.4
10.73 44.92 1025.1 85.4 476.81
9.38 40.46 1019.29 75.77 474.1
20.27 57.76 1016.66 75.76 450.71
24.82 66.48 1006.4 70.21 433.62
16.55 41.66 1011.45 55.53 465.14
20.73 59.87 1019.08 80.48 445.18
9.51 39.22 1015.3 72.41 474.12
8.63 43.79 1016.08 83.25 483.91
6.48 40.27 1010.55 82.12 486.68
14.95 43.52 1022.43 94.75 464.98
5.76 45.87 1010.83 95.79 481.4
10.94 39.04 1021.81 86.02 479.2
15.87 41.16 1005.85 78.29 463.86
12.42 38.25 1012.76 82.23 472.3
29.12 58.84 1001.31 52.86 446.51
29.12 51.43 1005.93 60.66 437.71
19.08 41.1 1001.96 62.77 458.94
31.06 67.17 1007.62 65.54 437.91
5.72 39.33 1009.96 95.4 490.76
26.52 65.06 1013.4 51.78 439.66
13.84 44.9 1007.58 63.62 463.27
13.03 39.52 1016.68 83.09 473.99
25.94 66.49 1012.83 61.81 433.38
16.64 53.82 1015.13 68.24 459.01
14.13 40.75 1016.05 72.41 471.44
13.65 39.28 1012.97 79.64 471.91
14.5 44.47 1028.2 66.95 465.15
19.8 51.19 1008.25 91.98 446.66
25.2 63.76 1009.78 64.96 438.15
20.66 51.19 1008.81 88.93 447.14
12.07 43.71 1025.53 85.62 472.32
25.64 70.72 1010.16 84.0 441.68
23.33 72.99 1009.33 89.41 440.04
29.41 64.05 1009.82 67.4 444.82
16.6 53.16 1014.5 76.75 457.26
27.53 72.58 1009.13 89.06 428.83
20.62 43.43 1009.93 64.02 449.07
26.02 71.94 1009.38 64.12 435.21
12.75 44.2 1017.59 81.22 471.03
12.87 48.04 1012.47 100.13 465.56
25.77 62.96 1019.86 58.07 442.83
14.84 41.48 1017.26 63.42 460.3
7.41 40.71 1023.07 83.32 474.25
8.87 41.82 1033.3 74.28 477.97
9.69 40.46 1019.1 71.91 472.16
16.17 46.97 1014.22 85.8 456.08
26.24 49.82 1014.9 55.58 452.41
13.78 43.22 1011.31 69.7 463.71
26.3 67.07 1006.26 63.79 433.72
17.37 57.76 1016.0 86.59 456.4
23.6 48.98 1015.41 48.28 448.43
8.3 36.08 1020.63 80.42 481.6
18.86 42.18 1001.16 98.58 457.07
22.12 49.39 1019.8 72.83 451.0
28.41 75.6 1018.48 56.07 440.28
29.42 71.32 1002.26 67.13 437.47
18.61 67.71 1004.07 84.49 443.57
27.57 69.84 1004.91 68.37 426.6
12.83 41.5 1013.12 86.07 470.87
9.64 39.85 1012.9 83.82 478.37
19.13 58.66 1013.32 74.86 453.92
15.92 40.56 1020.79 53.52 470.22
24.64 72.24 1011.37 80.61 434.54
27.62 63.9 1013.11 43.56 442.89
8.9 36.24 1013.29 89.35 479.03
9.55 43.99 1020.5 97.28 476.06
10.57 36.71 1022.62 80.49 473.88
19.8 57.25 1010.84 88.9 451.75
25.63 56.85 1012.68 49.7 439.2
24.7 58.46 1015.58 68.64 439.7
15.26 46.18 1013.68 98.58 463.6
20.06 52.84 1004.21 82.12 447.47
19.84 56.89 1013.23 78.32 447.92
11.49 44.63 1020.44 86.04 471.08
23.74 72.43 1007.99 91.36 437.55
22.62 51.3 1012.36 81.02 448.27
29.53 72.39 998.47 76.05 431.69
21.32 48.14 1016.57 71.81 449.09
20.3 58.46 1015.93 82.13 448.79
16.97 44.92 1025.21 74.27 460.21
12.07 41.17 1013.54 71.32 479.28
7.46 41.82 1032.67 74.59 483.11
19.2 54.2 1011.46 84.44 450.75
28.64 66.54 1010.43 43.39 437.97
13.56 41.48 1008.53 87.2 459.76
17.4 44.9 1020.5 77.11 457.75
14.08 40.1 1015.48 82.81 469.33
27.11 69.75 1009.74 85.67 433.28
20.92 70.02 1010.23 95.58 444.64
16.18 44.9 1021.3 74.46 463.1
15.57 44.68 1022.01 90.02 460.91
10.37 39.04 1023.95 81.93 479.35
19.6 59.21 1017.65 86.29 449.23
9.22 40.92 1021.83 85.43 474.51
27.76 72.99 1007.81 71.66 435.02
28.68 70.72 1009.43 71.33 435.45
20.95 48.14 1013.3 67.72 452.38
9.06 39.3 1019.73 84.23 480.41
9.21 39.72 1019.54 74.44 478.96
13.65 42.74 1026.58 71.48 468.87
31.79 76.2 1007.89 56.3 434.01
14.32 44.6 1013.85 68.13 466.36
26.28 75.23 1011.44 68.35 435.28
7.69 43.02 1014.51 85.23 486.46
14.44 40.1 1015.51 79.78 468.19
9.19 41.01 1022.14 98.98 468.37
13.35 41.39 1019.17 72.87 474.19
23.04 74.22 1009.52 90.93 440.32
4.83 38.44 1015.35 72.94 485.32
17.29 42.86 1014.38 72.3 464.27
8.73 36.18 1013.66 77.74 479.25
26.21 70.32 1007.0 78.29 430.4
23.72 58.62 1016.65 69.1 447.49
29.27 64.69 1006.85 55.79 438.23
10.4 40.43 1025.46 75.09 492.09
12.19 40.75 1015.13 88.98 475.36
20.4 54.9 1016.68 64.26 452.56
34.3 74.67 1015.98 25.89 427.84
27.56 68.08 1010.8 59.18 433.95
30.9 70.8 1008.48 67.48 435.27
14.85 58.59 1014.04 89.85 454.62
16.42 40.56 1020.36 50.62 472.17
16.45 63.31 1015.96 83.97 452.42
10.14 42.02 1003.19 96.51 472.17
9.53 41.44 1018.01 80.09 481.83
17.01 49.15 1021.83 84.02 458.78
23.94 62.08 1022.47 61.97 447.5
15.95 49.25 1019.04 88.51 463.4
11.15 41.26 1022.67 81.83 473.57
25.56 70.32 1009.07 90.63 433.72
27.16 66.44 1011.2 73.37 431.85
26.71 77.95 1012.13 77.5 433.47
29.56 74.22 1007.45 57.46 432.84
31.19 70.94 1007.29 51.91 436.6
6.86 41.17 1020.12 79.14 490.23
12.36 41.74 1020.58 69.24 477.16
32.82 68.31 1010.44 41.85 441.06
25.3 70.98 1007.22 95.1 440.86
8.71 41.82 1033.08 74.53 477.94
13.34 40.8 1026.56 64.85 474.47
14.2 43.02 1012.18 57.07 470.67
23.74 65.34 1013.7 62.9 447.31
16.9 44.88 1018.14 72.21 466.8
28.54 71.94 1007.4 65.99 430.91
30.15 69.88 1007.2 73.67 434.75
14.33 42.86 1010.82 88.59 469.52
25.57 59.43 1008.88 61.19 438.9
30.55 70.04 1010.51 49.37 429.56
28.04 74.33 1013.53 48.65 432.92
26.39 49.16 1005.68 56.18 442.87
15.3 41.76 1022.57 71.56 466.59
6.03 41.14 1028.04 87.46 479.61
13.49 44.63 1019.12 70.02 471.08
27.67 59.14 1016.51 61.2 433.37
24.19 65.48 1018.8 60.54 443.92
24.44 59.14 1016.74 71.82 443.5
29.86 64.79 1017.37 44.8 439.89
30.2 69.59 1008.9 67.32 434.66
7.99 41.38 1021.95 78.77 487.57
9.93 41.62 1013.76 96.02 464.64
11.03 42.32 1017.26 90.56 470.92
22.34 63.73 1014.37 83.19 444.39
25.33 48.6 1002.54 68.45 442.48
18.87 52.08 1005.25 99.19 449.61
25.97 69.34 1009.43 88.11 435.02
16.58 43.99 1021.81 79.29 458.67
14.35 46.18 1016.63 87.76 461.74
25.06 62.39 1008.09 82.56 438.31
13.85 48.92 1011.68 79.24 462.38
16.09 44.2 1019.39 67.24 460.56
26.34 59.21 1013.37 58.98 439.22
23.01 58.79 1009.71 84.22 444.64
26.39 71.25 999.8 89.12 430.34
31.32 71.29 1008.37 50.07 430.46
16.64 45.87 1009.02 98.86 456.79
13.42 41.23 994.17 95.79 468.82
20.06 44.9 1008.79 70.06 448.51
14.8 44.71 1014.67 41.71 470.77
12.59 41.14 1025.79 86.55 465.74
26.7 66.56 1005.31 71.97 430.21
19.78 50.32 1008.62 96.4 449.23
15.17 49.15 1021.91 91.73 461.89
21.71 61.45 1010.97 91.62 445.72
19.09 39.39 1013.36 59.14 466.13
19.76 51.19 1008.38 92.56 448.71
14.68 41.23 998.43 83.71 469.25
21.3 66.86 1013.04 55.43 450.56
16.73 39.64 1008.94 74.91 464.46
12.26 41.5 1014.87 89.41 471.13
14.77 48.06 1010.92 69.81 461.52
18.26 59.15 1012.04 86.01 451.09
27.1 79.74 1005.43 86.05 431.51
14.72 40.83 1009.65 80.98 469.8
26.3 51.43 1012.05 63.62 442.28
16.48 48.92 1011.84 64.16 458.67
17.99 43.79 1016.13 75.63 462.4
20.34 59.8 1015.18 80.21 453.54
25.53 62.96 1019.81 59.7 444.38
31.59 58.9 1003.39 47.6 440.52
30.8 69.14 1007.68 63.78 433.62
10.75 45.0 1023.68 89.37 481.96
19.3 44.9 1008.89 70.55 452.75
4.71 39.42 1026.4 84.42 481.28
23.1 66.05 1020.28 80.62 439.03
32.63 73.88 1005.64 52.56 435.75
26.63 74.16 1009.72 83.26 436.03
24.35 58.49 1011.03 70.64 445.6
15.11 56.03 1020.27 89.95 462.65
29.1 50.05 1005.87 51.53 438.66
21.24 50.32 1008.54 84.83 447.32
6.16 39.48 1004.85 59.68 484.55
7.36 41.01 1024.9 97.88 476.8
10.44 39.04 1023.99 85.03 480.34
26.76 48.41 1010.53 47.38 440.63
16.79 44.6 1014.27 48.08 459.48
10.76 40.43 1025.98 79.65 490.78
6.07 38.91 1019.25 83.39 483.56
27.33 73.18 1012.26 82.18 429.38
27.15 59.21 1013.49 51.71 440.27
22.35 51.43 1011.34 77.33 445.34
21.82 65.27 1013.86 72.81 447.43
21.11 69.94 1004.37 84.26 439.91
19.95 50.59 1016.11 73.23 459.27
7.45 39.61 1017.88 79.73 478.89
15.36 41.66 1012.41 62.32 466.7
15.65 43.5 1021.39 78.58 463.5
25.31 74.33 1015.04 79.88 436.21
25.88 63.47 1011.95 65.87 443.94
24.6 63.94 1012.87 80.28 439.63
22.58 41.54 1013.21 71.33 460.95
19.69 59.14 1015.99 70.33 448.69
25.85 75.08 1006.24 57.73 444.63
10.06 37.83 1005.49 99.46 473.51
18.59 39.54 1008.56 68.61 462.56
18.27 50.16 1011.07 95.91 451.76
8.85 40.43 1025.68 80.42 491.81
30.04 68.08 1011.04 51.01 429.52
26.06 49.02 1007.59 74.08 437.9
14.8 38.73 1003.18 80.73 467.54
23.93 64.45 1015.35 54.71 449.97
23.72 66.48 1003.61 73.75 436.62
11.44 40.55 1023.37 88.43 477.68
20.28 63.86 1016.04 74.66 447.26
27.9 63.13 1011.8 70.04 439.76
24.74 59.39 1015.23 74.64 437.49
14.8 58.2 1018.29 85.11 455.14
8.22 41.03 1021.76 82.97 485.5
27.56 66.93 1016.81 55.59 444.1
32.07 70.94 1006.91 49.9 432.33
9.53 44.03 1008.87 89.99 471.23
13.61 42.34 1017.93 91.61 463.89
22.2 51.19 1009.2 82.95 445.54
21.36 59.54 1007.99 92.62 446.09
23.25 63.86 1017.82 59.64 445.12
23.5 59.21 1018.29 63.0 443.31
8.46 39.66 1015.14 85.38 484.16
8.19 40.69 1019.86 85.23 477.76
30.67 71.29 1008.36 52.08 430.28
32.48 62.04 1010.39 38.05 446.48
8.99 36.66 1028.11 71.98 481.03
13.77 47.83 1007.41 90.66 466.07
19.05 67.32 1013.2 83.14 447.47
21.19 55.5 1019.83 65.22 455.93
10.12 40.0 1021.15 91.67 479.62
24.93 47.01 1014.28 66.04 455.06
8.47 40.46 1019.87 78.19 475.06
24.52 56.85 1012.59 54.47 438.89
28.55 69.84 1003.38 67.26 432.7
20.58 50.9 1011.89 72.56 452.6
18.31 46.21 1010.46 82.15 451.75
27.18 71.06 1008.16 86.32 430.66
4.43 38.91 1019.04 88.17 491.9
26.02 74.78 1010.04 72.78 439.82
15.75 39.0 1015.91 69.58 460.73
22.99 60.95 1015.14 69.86 449.7
25.52 59.15 1013.88 65.37 439.42
27.04 65.06 1013.33 52.37 439.84
6.42 35.57 1025.58 79.63 485.86
17.04 40.12 1011.81 83.14 458.1
10.79 39.82 1012.89 88.25 479.92
20.41 56.03 1019.94 55.85 458.29
7.36 40.07 1017.29 52.55 489.45
28.08 73.42 1012.17 62.74 434.0
24.74 69.13 1010.69 90.08 431.24
28.32 47.93 1003.26 54.5 439.5
16.71 40.56 1019.48 49.88 467.46
30.7 71.58 1010.0 48.96 429.27
18.42 58.95 1016.95 86.77 452.1
10.62 42.02 999.83 96.66 472.41
22.18 69.05 1002.75 70.84 442.14
22.38 49.3 1003.56 83.83 441.0
13.94 41.58 1020.76 68.22 463.07
21.24 60.84 1017.99 82.22 445.71
6.76 39.81 1017.11 87.9 483.16
26.73 68.84 1010.75 66.83 440.45
7.24 38.06 1020.6 85.36 481.83
10.84 40.62 1015.53 60.9 467.6
19.32 52.84 1004.29 83.51 450.88
29.0 69.13 1001.22 52.96 425.5
23.38 54.42 1013.95 73.02 451.87
31.17 69.51 1010.51 43.11 428.94
26.17 48.6 1002.59 61.41 439.86
30.9 73.42 1011.21 65.32 433.44
24.92 73.68 1015.12 93.68 438.23
32.77 71.32 1007.68 42.39 436.95
14.37 40.56 1021.67 68.18 470.19
8.36 40.22 1011.6 89.18 484.66
31.45 68.27 1007.56 64.79 430.81
31.6 73.17 1010.05 43.48 433.37
17.9 48.98 1014.17 80.4 453.02
20.35 50.9 1012.6 72.43 453.5
16.21 41.23 995.88 80.0 463.09
19.36 44.6 1016.25 45.65 464.56
21.04 65.46 1017.22 63.02 452.12
14.05 40.69 1015.66 74.39 470.9
23.48 64.15 1021.08 57.77 450.89
21.91 63.76 1009.85 76.8 445.04
24.42 63.07 1011.49 67.39 444.72
14.26 40.92 1022.07 73.96 460.38
21.38 58.33 1013.05 72.75 446.8
15.71 44.06 1018.34 71.69 465.05
5.78 40.62 1016.55 84.98 484.13
6.77 39.81 1017.01 87.68 488.27
23.84 49.21 1013.85 50.36 447.09
21.17 58.16 1017.16 68.11 452.02
19.94 58.96 1014.16 66.27 455.55
8.73 41.92 1029.41 89.72 480.99
16.39 41.67 1012.96 61.07 467.68
res12: Long = 9568
+--------+--------------------+-----------+
|database|           tableName|isTemporary|
+--------+--------------------+-----------+
| default|power_plant_predi...|      false|
| default|    sentimentlex_csv|      false|
| default|        simple_range|      false|
| default|  social_media_usage|      false|
| default|social_media_usag...|      false|
+--------+--------------------+-----------+
+------------------------------------------------------------+--------+-----------+---------+-----------+
|name                                                        |database|description|tableType|isTemporary|
+------------------------------------------------------------+--------+-----------+---------+-----------+
|power_plant_predictions                                     |default |null       |MANAGED  |false      |
|sentimentlex_csv                                            |default |null       |EXTERNAL |false      |
|simple_range                                                |default |null       |MANAGED  |false      |
|social_media_usage                                          |default |null       |MANAGED  |false      |
|social_media_usage_table_partitionedbyplatformbucketedbydate|default |null       |MANAGED  |false      |
+------------------------------------------------------------+--------+-----------+---------+-----------+
+-------+---------------------+-------------------------+
|name   |description          |locationUri              |
+-------+---------------------+-------------------------+
|default|Default Hive database|dbfs:/user/hive/warehouse|
+-------+---------------------+-------------------------+

Step 6: Data Modeling

Now let's model our data to predict what the power output will be given a set of sensor readings

Our first model will be based on simple linear regression since we saw some linear patterns in our data based on the scatter plots during the exploration stage.

+--------+--------------------+-----------+
|database|           tableName|isTemporary|
+--------+--------------------+-----------+
| default|power_plant_predi...|      false|
| default|    sentimentlex_csv|      false|
| default|        simple_range|      false|
| default|  social_media_usage|      false|
| default|social_media_usag...|      false|
|        |   power_plant_table|       true|
+--------+--------------------+-----------+
AT V AP RH PE
14.96 41.76 1024.07 73.17 463.26
25.18 62.96 1020.04 59.08 444.37
5.11 39.4 1012.16 92.14 488.56
20.86 57.32 1010.24 76.64 446.48
10.82 37.5 1009.23 96.62 473.9
26.27 59.44 1012.23 58.77 443.67
15.89 43.96 1014.02 75.24 467.35
9.48 44.71 1019.12 66.43 478.42
14.64 45.0 1021.78 41.25 475.98
11.74 43.56 1015.14 70.72 477.5
17.99 43.72 1008.64 75.04 453.02
20.14 46.93 1014.66 64.22 453.99
24.34 73.5 1011.31 84.15 440.29
25.71 58.59 1012.77 61.83 451.28
26.19 69.34 1009.48 87.59 433.99
21.42 43.79 1015.76 43.08 462.19
18.21 45.0 1022.86 48.84 467.54
11.04 41.74 1022.6 77.51 477.2
14.45 52.75 1023.97 63.59 459.85
13.97 38.47 1015.15 55.28 464.3
17.76 42.42 1009.09 66.26 468.27
5.41 40.07 1019.16 64.77 495.24
7.76 42.28 1008.52 83.31 483.8
27.23 63.9 1014.3 47.19 443.61
27.36 48.6 1003.18 54.93 436.06
27.47 70.72 1009.97 74.62 443.25
14.6 39.31 1011.11 72.52 464.16
7.91 39.96 1023.57 88.44 475.52
5.81 35.79 1012.14 92.28 484.41
30.53 65.18 1012.69 41.85 437.89
23.87 63.94 1019.02 44.28 445.11
26.09 58.41 1013.64 64.58 438.86
29.27 66.85 1011.11 63.25 440.98
27.38 74.16 1010.08 78.61 436.65
24.81 63.94 1018.76 44.51 444.26
12.75 44.03 1007.29 89.46 465.86
24.66 63.73 1011.4 74.52 444.37
16.38 47.45 1010.08 88.86 450.69
13.91 39.35 1014.69 75.51 469.02
23.18 51.3 1012.04 78.64 448.86
22.47 47.45 1007.62 76.65 447.14
13.39 44.85 1017.24 80.44 469.18
9.28 41.54 1018.33 79.89 482.8
11.82 42.86 1014.12 88.28 476.7
10.27 40.64 1020.63 84.6 474.99
22.92 63.94 1019.28 42.69 444.22
16.0 37.87 1020.24 78.41 461.33
21.22 43.43 1010.96 61.07 448.06
13.46 44.71 1014.51 50.0 474.6
9.39 40.11 1029.14 77.29 473.05
31.07 73.5 1010.58 43.66 432.06
12.82 38.62 1018.71 83.8 467.41
32.57 78.92 1011.6 66.47 430.12
8.11 42.18 1014.82 93.09 473.62
13.92 39.39 1012.94 80.52 471.81
23.04 59.43 1010.23 68.99 442.99
27.31 64.44 1014.65 57.27 442.77
5.91 39.33 1010.18 95.53 491.49
25.26 61.08 1013.68 71.72 447.46
27.97 58.84 1002.25 57.88 446.11
26.08 52.3 1007.03 63.34 442.44
29.01 65.71 1013.61 48.07 446.22
12.18 40.1 1016.67 91.87 471.49
13.76 45.87 1008.89 87.27 463.5
25.5 58.79 1016.02 64.4 440.01
28.26 65.34 1014.56 43.4 441.03
21.39 62.96 1019.49 72.24 452.68
7.26 40.69 1020.43 90.22 474.91
10.54 34.03 1018.71 74.0 478.77
27.71 74.34 998.14 71.85 434.2
23.11 68.3 1017.83 86.62 437.91
7.51 41.01 1024.61 97.41 477.61
26.46 74.67 1016.65 84.44 431.65
29.34 74.34 998.58 81.55 430.57
10.32 42.28 1008.82 75.66 481.09
22.74 61.02 1009.56 79.41 445.56
13.48 39.85 1012.71 58.91 475.74
25.52 69.75 1010.36 90.06 435.12
21.58 67.25 1017.39 79.0 446.15
27.66 76.86 1001.31 69.47 436.64
26.96 69.45 1013.89 51.47 436.69
12.29 42.18 1016.53 83.13 468.75
15.86 43.02 1012.18 40.33 466.6
13.87 45.08 1024.42 81.69 465.48
24.09 73.68 1014.93 94.55 441.34
20.45 69.45 1012.53 91.81 441.83
15.07 39.3 1019.0 63.62 464.7
32.72 69.75 1009.6 49.35 437.99
18.23 58.96 1015.55 69.61 459.12
35.56 68.94 1006.56 38.75 429.69
18.36 51.43 1010.57 90.17 459.8
26.35 64.05 1009.81 81.24 433.63
25.92 60.95 1014.62 48.46 442.84
8.01 41.66 1014.49 76.72 485.13
19.63 52.72 1025.09 51.16 459.12
20.02 67.32 1012.05 76.34 445.31
10.08 40.72 1022.7 67.3 480.8
27.23 66.48 1005.23 52.38 432.55
23.37 63.77 1013.42 76.44 443.86
18.74 59.21 1018.3 91.55 449.77
14.81 43.69 1017.19 71.9 470.71
23.1 51.3 1011.93 80.05 452.17
10.72 41.38 1021.6 63.77 478.29
29.46 71.94 1006.96 62.26 428.54
8.1 40.64 1020.66 89.04 478.27
27.29 62.66 1007.63 58.02 439.58
17.1 49.69 1005.53 81.82 457.32
11.49 44.2 1018.79 91.14 475.51
23.69 65.59 1010.85 88.92 439.66
13.51 40.89 1011.03 84.83 471.99
9.64 39.35 1015.1 91.76 479.81
25.65 78.92 1010.83 86.56 434.78
21.59 61.87 1011.18 57.21 446.58
27.98 58.33 1013.92 54.25 437.76
18.8 39.72 1001.24 63.8 459.36
18.28 44.71 1016.99 33.71 462.28
13.55 43.48 1016.08 67.25 464.33
22.99 46.21 1010.71 60.11 444.36
23.94 59.39 1014.32 74.55 438.64
13.74 34.03 1018.69 67.34 470.49
21.3 41.1 1001.86 42.75 455.13
27.54 66.93 1017.06 55.2 450.22
24.81 63.73 1009.34 83.61 440.43
4.97 42.85 1014.02 88.78 482.98
15.22 50.88 1014.19 100.12 460.44
23.88 54.2 1012.81 64.52 444.97
33.01 68.67 1005.2 51.41 433.94
25.98 73.18 1012.28 85.78 439.73
28.18 73.88 1005.89 75.41 434.48
21.67 60.84 1017.93 81.63 442.33
17.67 45.09 1014.26 51.92 457.67
21.37 57.76 1018.8 70.12 454.66
28.69 67.25 1017.71 53.83 432.21
16.61 43.77 1012.25 77.23 457.66
27.91 63.76 1010.27 65.67 435.21
20.97 47.43 1007.64 71.18 448.22
10.8 41.66 1013.79 81.96 475.51
20.61 62.91 1013.24 79.54 446.53
25.45 57.32 1011.7 47.09 441.3
30.16 69.34 1007.67 57.69 433.54
4.99 39.04 1020.45 78.89 472.52
10.51 44.78 1012.59 85.29 474.77
33.79 69.05 1001.62 40.13 435.1
21.34 59.8 1016.92 77.06 450.74
23.4 65.06 1014.32 67.38 442.7
32.21 68.14 1003.34 62.44 426.56
14.26 42.32 1016.0 77.43 463.71
27.71 66.93 1016.85 58.77 447.06
21.95 57.76 1018.02 67.72 452.27
25.76 63.94 1018.49 42.14 445.78
23.68 68.3 1017.93 84.16 438.65
8.28 40.77 1011.55 89.79 480.15
23.44 62.52 1016.46 67.21 447.19
25.32 48.41 1008.47 72.14 443.04
3.94 39.9 1008.06 97.49 488.81
17.3 57.76 1016.26 87.74 455.75
18.2 49.39 1018.83 96.3 455.86
21.43 46.97 1013.94 61.25 457.68
11.16 40.05 1014.95 88.38 479.11
30.38 74.16 1007.44 74.77 432.84
23.36 62.52 1016.18 68.18 448.37
21.69 47.45 1007.56 77.2 447.06
23.62 49.21 1014.1 49.54 443.53
21.87 61.45 1011.13 92.22 445.21
29.25 66.51 1015.53 33.65 441.7
20.03 66.86 1013.05 64.59 450.93
18.14 49.78 1002.95 100.09 451.44
24.23 56.89 1012.32 68.04 441.29
18.11 44.85 1014.48 48.94 458.85
6.57 43.65 1018.24 74.47 481.46
12.56 43.41 1016.93 81.02 467.19
13.4 41.58 1020.5 71.17 461.54
27.1 52.84 1006.28 53.85 439.08
14.28 42.74 1028.79 70.67 467.22
16.29 44.34 1019.49 59.36 468.8
31.24 71.98 1004.66 57.17 426.93
10.57 37.73 1024.36 70.29 474.65
13.8 44.21 1022.93 83.37 468.97
25.3 71.58 1010.18 87.36 433.97
18.06 50.16 1009.52 100.09 450.53
25.42 59.04 1011.98 68.78 444.51
15.07 40.69 1015.29 70.98 469.03
11.75 71.14 1019.36 75.68 466.56
20.23 52.05 1012.15 47.49 457.57
27.31 59.54 1006.24 71.99 440.13
28.57 69.84 1003.57 66.55 433.24
17.9 43.72 1008.64 74.73 452.55
23.83 71.37 1002.04 64.78 443.29
27.92 74.99 1005.47 75.13 431.76
17.34 44.78 1007.81 56.38 454.97
17.94 63.07 1012.42 94.35 456.7
6.4 39.9 1007.75 86.55 486.03
11.78 39.96 1011.37 82.95 472.79
20.28 57.25 1010.12 88.42 452.03
21.04 54.2 1012.26 85.61 443.41
25.11 67.32 1014.49 58.39 441.93
30.28 70.98 1007.51 74.28 432.64
8.14 36.24 1013.15 87.85 480.25
16.86 39.63 1004.47 83.5 466.68
6.25 40.07 1020.19 65.24 494.39
22.35 54.42 1012.46 75.01 454.72
17.98 56.85 1012.28 84.52 448.71
21.19 42.48 1013.43 80.52 469.76
20.94 44.89 1009.64 75.14 450.71
24.23 58.79 1009.8 75.75 444.01
19.18 58.2 1017.46 76.72 453.2
20.88 57.85 1012.39 85.47 450.87
23.67 63.86 1019.67 57.95 441.73
14.12 39.52 1018.41 78.32 465.09
25.23 64.63 1020.59 52.2 447.28
6.54 39.33 1011.54 93.69 491.16
20.08 62.52 1017.99 75.74 450.98
24.67 63.56 1013.75 67.56 446.3
27.82 79.74 1008.37 69.46 436.48
15.55 42.03 1017.41 74.58 460.84
24.26 69.51 1013.43 53.23 442.56
13.45 41.49 1020.19 88.72 467.3
11.06 40.64 1021.47 96.16 479.13
24.91 52.3 1008.72 68.26 441.15
22.39 59.04 1011.78 86.39 445.52
11.95 40.69 1015.62 85.34 475.4
14.85 40.69 1014.91 72.64 469.3
10.11 41.62 1017.17 97.82 463.57
23.67 68.67 1006.71 77.22 445.32
16.14 44.21 1020.36 80.59 461.03
15.11 43.13 1014.99 46.91 466.74
24.14 59.87 1018.47 57.76 444.04
30.08 67.25 1017.6 53.09 434.01
14.77 44.9 1020.5 84.31 465.23
27.6 69.34 1009.63 71.58 440.6
13.89 44.84 1023.66 92.97 466.74
26.85 75.6 1017.43 74.55 433.48
12.41 40.96 1023.36 78.96 473.59
13.08 41.74 1020.75 64.44 474.81
18.93 44.06 1017.58 68.23 454.75
20.5 49.69 1009.6 70.81 452.94
30.72 69.13 1009.94 61.66 435.83
7.55 39.22 1014.53 77.76 482.19
13.49 44.47 1030.46 69.49 466.66
15.62 40.12 1013.03 96.26 462.59
24.8 64.63 1020.69 55.74 447.82
10.03 41.62 1014.55 95.61 462.73
22.43 63.21 1012.06 84.75 447.98
14.95 39.31 1009.15 75.3 462.72
24.78 58.46 1016.82 67.5 442.42
23.2 48.41 1008.64 80.92 444.69
14.01 39.0 1016.73 79.23 466.7
19.4 64.63 1020.38 81.1 453.84
30.15 67.32 1013.83 32.8 436.92
6.91 36.08 1021.82 84.31 486.37
29.04 60.07 1015.42 46.15 440.43
26.02 63.07 1010.94 53.96 446.82
5.89 39.48 1005.11 59.83 484.91
26.52 71.64 1008.27 75.3 437.76
28.53 68.08 1013.27 42.53 438.91
16.59 39.54 1007.97 70.58 464.19
22.95 67.79 1009.89 91.69 442.19
23.96 47.43 1008.38 63.55 446.86
17.48 44.2 1018.89 61.51 457.15
6.69 43.65 1020.14 69.55 482.57
10.25 41.26 1007.44 98.08 476.03
28.87 72.58 1008.69 79.34 428.89
12.04 40.23 1018.07 81.28 472.7
22.58 52.3 1009.04 78.99 445.6
15.12 52.05 1014.63 80.38 464.78
25.48 58.95 1017.02 51.16 440.42
27.87 70.79 1003.96 72.17 428.41
23.72 70.47 1010.65 75.39 438.5
25.0 59.43 1007.84 68.91 438.28
8.42 40.64 1022.35 96.38 476.29
22.46 58.49 1011.5 70.54 448.46
29.92 57.19 1008.62 45.8 438.99
11.68 39.22 1017.9 57.95 471.8
14.04 42.44 1012.74 81.89 471.81
19.86 59.14 1016.12 69.32 449.82
25.99 68.08 1013.13 59.14 442.14
23.42 58.79 1009.74 81.54 441.46
10.6 40.22 1011.37 85.81 477.62
20.97 61.87 1011.45 65.41 446.76
14.14 39.82 1012.46 81.15 472.52
8.56 40.71 1021.27 95.87 471.58
24.86 72.39 1001.15 90.24 440.85
29.0 77.54 1011.33 75.13 431.37
27.59 71.97 1008.64 88.22 437.33
10.45 40.71 1015.68 81.48 469.22
8.51 40.78 1023.51 89.84 471.11
29.82 66.51 1010.98 43.57 439.17
22.56 62.26 1012.11 63.16 445.33
11.38 39.22 1018.62 57.14 473.71
20.25 57.76 1016.28 77.76 452.66
22.42 59.43 1007.12 90.56 440.99
14.85 38.91 1014.48 60.98 467.42
25.62 58.82 1010.02 70.31 444.14
19.85 56.53 1020.57 74.05 457.17
13.67 54.3 1015.92 75.42 467.87
24.39 70.72 1009.78 82.25 442.04
16.07 44.58 1019.52 67.95 471.36
11.6 39.1 1009.81 100.09 460.7
31.38 70.83 1010.35 47.28 431.33
29.91 76.86 998.59 72.41 432.6
19.67 59.39 1014.07 77.67 447.61
27.18 64.79 1016.27 63.7 443.87
21.39 52.3 1009.2 79.77 446.87
10.45 41.01 1020.57 93.84 465.74
19.46 56.89 1014.02 84.95 447.86
23.55 62.96 1020.16 70.16 447.65
23.35 63.47 1011.78 84.24 437.87
9.26 41.66 1016.87 73.32 483.51
10.3 41.46 1018.21 86.17 479.65
20.94 58.16 1016.88 65.43 455.16
23.13 71.25 1002.49 94.59 431.91
12.77 41.5 1014.13 86.8 470.68
28.29 69.13 1009.29 58.18 429.28
19.13 59.21 1018.32 89.66 450.81
24.44 73.5 1011.49 87.39 437.73
20.32 44.6 1015.16 36.35 460.21
20.54 69.05 1001.6 79.62 442.86
12.16 45.0 1021.51 50.52 482.99
28.09 65.27 1013.27 51.96 440.0
9.25 41.82 1033.25 74.73 478.48
21.75 49.82 1015.01 78.33 455.28
23.7 66.56 1002.07 85.19 436.94
16.22 37.87 1022.36 83.13 461.06
24.75 69.45 1013.97 53.49 438.28
10.48 39.58 1011.81 88.86 472.61
29.53 70.79 1003.7 60.89 426.85
12.59 39.72 1017.76 61.14 470.18
23.5 54.42 1012.31 68.29 455.38
29.01 66.56 1006.44 57.62 428.32
9.75 42.49 1010.57 83.63 480.35
19.55 56.53 1020.2 78.1 455.56
21.05 58.33 1013.14 66.34 447.66
24.72 68.67 1006.74 79.02 443.06
21.19 58.86 1014.19 68.96 452.43
10.77 41.54 1019.94 71.13 477.81
28.68 73.77 1004.72 87.01 431.66
29.87 73.91 1004.53 74.3 431.8
22.99 68.67 1006.65 77.62 446.67
24.66 60.29 1018.0 59.56 445.26
32.63 69.89 1013.85 41.66 425.72
31.38 72.29 1008.73 73.27 430.58
23.87 60.27 1018.94 77.16 439.86
25.6 59.15 1013.31 67.02 441.11
27.62 71.14 1011.6 52.8 434.72
30.1 67.45 1014.23 39.04 434.01
12.19 41.17 1019.43 65.47 475.64
13.11 41.58 1020.43 74.32 460.44
28.29 68.67 1005.46 69.22 436.4
13.45 40.73 1018.7 93.88 461.03
10.98 41.54 1019.94 69.83 479.08
26.48 69.14 1009.31 84.11 435.76
13.07 45.51 1015.22 78.65 460.14
25.56 75.6 1017.37 69.31 442.2
22.68 50.78 1008.83 70.3 447.69
28.86 73.67 1006.65 68.23 431.15
22.7 63.56 1014.32 71.76 445.0
27.89 73.21 1001.32 85.88 431.59
13.78 44.47 1027.94 71.09 467.22
28.14 51.43 1012.16 52.67 445.33
11.8 45.09 1013.21 89.68 470.57
10.71 39.61 1018.72 73.66 473.77
24.54 60.29 1017.42 58.94 447.67
11.54 40.05 1014.78 87.05 474.29
29.47 71.32 1008.07 67.0 437.14
29.24 69.05 1003.12 43.18 432.56
14.51 41.79 1009.72 80.62 459.14
22.91 60.07 1016.03 59.72 446.19
27.02 71.77 1006.38 72.1 428.1
13.49 44.47 1030.18 69.15 468.46
30.24 66.75 1017.95 55.66 435.02
23.19 48.6 1002.38 61.19 445.52
17.73 40.55 1003.36 74.62 462.69
18.62 61.27 1019.26 73.35 455.75
12.85 40.0 1015.89 68.85 463.74
32.33 69.68 1011.95 39.89 439.79
25.09 58.95 1016.99 53.16 443.26
29.45 69.13 1009.3 52.97 432.04
16.91 43.96 1013.32 79.87 465.86
14.09 45.87 1009.05 84.09 465.6
10.73 25.36 1009.35 100.15 469.43
23.2 49.3 1003.4 79.77 440.75
8.21 38.91 1015.82 88.99 481.32
9.3 40.56 1022.64 76.14 479.87
16.97 39.16 1005.7 69.13 458.59
23.69 71.97 1009.62 93.03 438.62
25.13 59.44 1012.38 77.92 445.59
9.86 43.56 1015.13 74.89 481.87
11.33 41.5 1013.58 88.7 475.01
26.95 48.41 1008.53 62.94 436.54
15.0 40.66 1016.28 89.62 456.63
20.76 62.52 1015.63 81.04 451.69
14.29 39.59 1010.93 94.53 463.04
19.74 67.71 1007.68 64.02 446.1
26.68 59.92 1009.94 70.57 438.67
14.24 41.4 1019.7 70.32 466.88
21.98 48.41 1008.42 84.86 444.6
22.75 59.39 1015.4 81.41 440.26
8.34 40.96 1023.28 89.45 483.92
11.8 41.2 1017.18 82.71 475.19
8.81 44.68 1023.06 93.93 479.24
30.05 73.68 1014.95 70.6 434.92
16.01 65.46 1014.0 87.68 454.16
21.75 58.79 1012.42 87.58 447.58
13.94 41.26 1021.67 74.4 467.9
29.25 69.13 1010.27 67.35 426.29
22.33 45.87 1007.8 63.61 447.02
16.43 41.79 1005.47 76.89 455.85
11.5 40.22 1010.31 78.08 476.46
23.53 68.94 1007.53 69.17 437.48
21.86 49.21 1014.61 53.31 452.77
6.17 39.33 1012.57 93.32 491.54
30.19 64.79 1017.22 42.47 438.41
11.67 41.93 1019.81 82.58 476.1
15.34 36.99 1007.87 94.59 464.58
11.5 40.78 1023.91 86.31 467.74
25.53 57.17 1010.0 72.57 442.12
21.27 57.5 1014.53 80.76 453.34
28.37 69.13 1010.44 71.93 425.29
28.39 51.43 1011.74 47.54 449.63
13.78 45.78 1025.27 95.72 462.88
14.6 42.32 1015.71 77.03 464.67
5.1 35.57 1027.17 80.49 489.96
7.0 38.08 1020.27 77.67 482.38
26.3 77.95 1009.45 78.72 437.95
30.56 71.98 1004.74 58.77 429.2
21.09 46.63 1013.03 74.8 453.34
28.21 70.02 1010.58 51.34 442.47
15.84 49.69 1015.14 90.41 462.6
10.03 40.96 1024.57 91.1 478.79
20.37 52.05 1012.34 62.57 456.11
21.19 50.16 1005.81 84.27 450.33
33.73 69.88 1007.21 42.93 434.83
29.87 73.68 1015.1 40.96 433.43
19.62 62.96 1020.76 76.53 456.02
9.93 40.67 1018.08 69.74 485.23
9.43 37.14 1013.03 74.99 473.57
14.24 39.58 1011.17 70.45 469.94
12.97 49.83 1008.69 91.49 452.07
7.6 41.04 1021.82 88.97 475.32
8.39 36.24 1013.39 89.13 480.69
25.41 48.06 1013.12 46.52 444.01
18.43 56.03 1020.41 60.55 465.17
10.31 39.82 1012.87 88.71 480.61
11.29 41.5 1013.39 89.15 476.04
22.61 49.3 1003.51 83.02 441.76
29.34 71.98 1005.19 75.19 428.24
18.87 67.71 1004.0 87.35 444.77
13.21 45.87 1008.58 85.66 463.1
11.3 44.6 1018.19 91.66 470.5
29.23 72.99 1007.04 63.47 431.0
27.76 69.4 1004.27 72.25 430.68
29.26 67.17 1006.6 70.58 436.42
25.72 49.82 1016.19 60.1 452.33
23.43 63.94 1010.64 89.29 440.16
25.6 63.76 1010.18 67.43 435.75
22.3 44.57 1008.48 67.58 449.74
27.91 72.24 1010.74 70.8 430.73
30.35 77.17 1009.55 63.62 432.75
21.78 47.43 1007.88 66.68 446.79
7.19 41.39 1018.12 90.76 486.35
20.88 59.8 1015.66 75.34 453.18
24.19 50.23 1015.73 59.77 458.31
9.98 41.54 1019.7 80.79 480.26
23.47 51.3 1011.89 74.1 448.65
26.35 49.5 1012.67 41.34 458.41
29.89 64.69 1006.37 58.78 435.39
19.29 50.16 1010.49 97.78 450.21
17.48 43.14 1018.68 74.85 459.59
25.21 75.6 1017.19 69.84 445.84
23.3 48.78 1018.17 75.36 441.08
15.42 37.85 1009.89 85.8 467.33
21.44 63.09 1016.56 90.11 444.19
29.45 68.27 1007.96 61.63 432.96
29.69 47.93 1002.85 44.76 438.09
15.52 36.99 1006.86 89.7 467.9
11.47 43.67 1012.68 72.51 475.72
9.77 34.69 1027.72 74.98 477.51
22.6 69.84 1006.37 79.59 435.13
8.24 39.61 1017.99 78.42 477.9
17.01 44.2 1019.18 61.23 457.26
19.64 44.6 1015.88 47.56 467.53
10.61 41.58 1021.08 93.06 465.15
12.04 40.1 1014.42 89.65 474.28
29.19 65.71 1013.85 50.5 444.49
21.75 45.09 1014.15 44.84 452.84
23.66 77.54 1008.5 85.32 435.38
27.05 75.33 1003.88 82.94 433.57
29.63 69.71 1009.04 67.26 435.27
18.2 39.63 1005.35 79.05 468.49
32.22 70.8 1009.9 62.03 433.07
26.88 73.56 1004.85 94.36 430.63
29.05 65.74 1013.29 60.02 440.74
8.9 39.96 1026.31 95.46 474.49
18.93 48.6 1005.72 84.92 449.74
27.49 63.76 1010.09 62.8 436.73
23.1 70.79 1006.53 90.81 434.58
11.22 43.13 1017.24 80.9 473.93
31.97 79.74 1007.03 55.84 435.99
13.32 43.22 1009.45 75.3 466.83
31.68 68.24 1005.29 37.34 427.22
23.69 63.77 1013.39 79.5 444.07
13.83 41.49 1020.11 87.29 469.57
18.32 66.51 1015.18 81.5 459.89
11.05 40.71 1024.91 76.42 479.59
22.03 64.69 1007.21 75.75 440.92
10.23 41.46 1020.45 84.95 480.87
23.92 66.54 1009.93 62.37 441.9
29.38 69.68 1011.35 49.25 430.2
17.35 42.86 1014.62 74.16 465.16
9.81 44.45 1021.19 90.55 471.32
4.97 40.64 1020.91 94.28 485.43
5.15 40.07 1012.27 63.31 495.35
21.54 58.49 1010.85 78.9 449.12
7.94 42.02 1006.22 90.97 480.53
18.77 50.66 1014.89 87.34 457.07
21.69 69.94 1010.7 80.8 443.67
10.07 44.68 1023.44 90.95 477.52
13.83 39.64 1012.52 69.97 472.95
10.45 39.69 1003.92 89.45 472.54
11.56 40.71 1015.85 76.08 469.17
23.64 70.04 1011.09 83.35 435.21
10.48 40.22 1004.81 92.16 477.78
13.09 39.85 1012.86 58.42 475.89
10.67 40.23 1017.75 85.06 483.9
12.57 39.16 1016.53 88.91 476.2
14.45 43.34 1015.47 83.33 462.16
14.22 37.85 1011.24 88.49 471.05
6.97 41.26 1010.6 96.88 484.71
20.61 63.86 1015.43 73.86 446.34
14.67 42.28 1007.21 65.17 469.02
29.06 72.86 1004.23 69.41 432.12
14.38 40.1 1015.51 81.23 467.28
32.51 69.98 1013.29 54.07 429.66
11.79 45.09 1013.16 89.17 469.49
8.65 40.56 1023.23 78.85 485.87
9.75 40.81 1026.0 84.44 481.95
9.11 40.02 1031.1 83.02 479.03
23.39 69.13 1010.99 90.66 434.5
14.3 54.3 1015.16 75.29 464.9
17.49 63.94 1020.02 82.6 452.71
31.1 69.51 1010.84 45.4 429.74
19.77 56.65 1020.67 66.33 457.09
28.61 72.29 1011.61 45.33 446.77
13.52 41.48 1014.46 67.12 460.76
13.52 40.83 1008.31 84.14 471.95
17.57 46.21 1014.09 80.81 453.29
28.18 60.07 1016.34 49.13 441.61
14.29 46.18 1017.01 87.29 464.73
18.12 43.69 1016.91 52.95 464.68
31.27 73.91 1003.72 68.92 430.59
26.24 77.95 1014.19 85.21 438.01
7.44 41.04 1021.84 88.56 479.08
29.78 74.78 1009.28 55.09 436.39
23.37 65.46 1016.25 48.64 447.07
10.62 39.58 1011.9 87.85 479.91
5.84 43.02 1013.88 87.42 489.05
14.51 53.82 1016.46 62.75 463.17
11.31 42.02 1001.18 94.86 471.26
11.25 40.67 1011.64 63.54 480.49
9.18 39.42 1025.41 69.46 473.78
19.82 58.16 1016.76 74.66 455.5
24.77 58.41 1013.78 80.57 446.27
9.66 41.06 1021.21 84.7 482.2
21.96 59.8 1016.72 72.6 452.48
18.59 43.14 1011.92 52.63 464.48
24.75 69.89 1015.29 82.01 438.1
24.37 63.47 1012.77 75.22 445.6
29.6 67.79 1010.37 51.05 442.43
25.32 61.25 1011.56 80.1 436.67
16.15 41.85 1016.54 81.58 466.56
15.74 71.14 1019.65 65.94 457.29
5.97 36.25 1029.65 86.74 487.03
15.84 52.72 1026.45 62.57 464.93
14.84 44.63 1019.28 57.37 466.0
12.25 48.79 1017.44 88.91 469.52
27.38 70.04 1011.18 72.26 428.88
8.76 41.48 1018.49 74.98 474.3
15.54 39.31 1009.69 71.19 461.06
18.71 39.39 1014.09 62.82 465.57
13.06 41.78 1012.3 55.31 467.67
12.72 40.71 1016.02 71.57 466.99
19.83 39.39 1013.73 59.16 463.72
27.23 49.16 1004.03 40.8 443.78
24.27 68.28 1005.43 67.63 445.23
11.8 40.66 1017.13 97.2 464.43
6.76 36.25 1028.31 91.16 484.36
25.99 63.07 1012.5 64.81 442.16
16.3 39.63 1004.64 85.61 464.11
16.5 49.39 1018.35 93.42 462.48
10.59 42.49 1009.59 77.36 477.49
26.05 65.59 1012.78 67.03 437.04
19.5 40.79 1003.8 89.45 457.09
22.21 45.01 1012.22 54.84 450.6
17.86 45.0 1023.25 53.48 465.78
29.96 70.04 1010.15 54.47 427.1
19.08 44.63 1020.14 43.36 459.81
23.59 47.43 1006.64 48.92 447.36
3.38 39.64 1011.0 81.22 488.92
26.39 66.49 1012.96 60.35 433.36
8.99 39.04 1021.99 75.98 483.35
10.91 41.04 1026.57 74.24 469.53
13.08 39.82 1012.27 85.21 476.96
23.95 58.46 1017.5 68.46 440.75
15.64 43.71 1024.51 78.31 462.55
18.78 54.2 1012.05 89.25 448.04
20.65 50.59 1016.22 68.57 455.24
4.96 40.07 1011.8 67.38 494.75
23.51 57.32 1012.55 53.6 444.58
5.99 35.79 1011.56 91.69 484.82
23.65 66.05 1019.6 78.21 442.9
5.17 39.33 1009.68 94.19 485.46
26.38 49.5 1012.82 37.19 457.81
6.02 43.65 1013.85 83.53 481.92
23.2 61.02 1009.63 79.45 443.23
8.57 39.69 1000.91 99.9 474.29
30.72 71.58 1009.98 50.39 430.46
21.52 50.66 1013.56 74.33 455.71
22.93 62.26 1011.25 83.66 438.34
5.71 41.31 1003.24 89.48 485.83
18.62 44.06 1017.76 64.59 452.82
27.88 68.94 1007.68 75.68 435.04
22.32 59.8 1016.82 64.18 451.21
14.55 42.74 1028.41 70.09 465.81
17.83 44.92 1025.04 70.58 458.42
9.68 39.96 1026.09 99.28 470.22
19.41 49.39 1020.84 81.89 449.24
13.22 44.92 1023.84 87.99 471.43
12.24 44.92 1023.74 88.21 473.26
19.21 58.49 1011.7 91.29 452.82
29.74 70.32 1008.1 52.72 432.69
23.28 60.84 1017.91 67.5 444.13
8.02 41.92 1029.8 92.05 467.21
22.47 48.6 1002.33 63.23 445.98
27.51 73.77 1002.42 90.88 436.91
17.51 44.9 1009.05 74.91 455.01
23.22 66.56 1002.47 85.39 437.11
11.73 40.64 1020.68 96.98 477.06
21.19 67.71 1006.65 56.28 441.71
5.48 40.07 1019.63 65.62 495.76
24.26 66.44 1011.33 55.32 445.63
12.32 41.62 1012.88 88.88 464.72
31.26 68.94 1005.94 39.49 438.03
32.09 72.86 1003.47 54.59 434.78
24.98 60.32 1015.63 57.19 444.67
27.48 61.41 1012.2 45.06 452.24
21.04 45.09 1014.19 40.62 450.92
27.75 70.4 1006.65 90.21 436.53
22.79 71.77 1005.75 90.91 435.53
24.22 68.51 1013.23 74.96 440.01
27.06 64.45 1008.72 54.21 443.1
29.25 71.94 1007.18 63.62 427.49
26.86 68.08 1012.99 50.04 436.25
29.64 67.79 1009.99 51.23 440.74
19.92 63.31 1015.02 82.71 443.54
18.5 51.43 1010.82 92.04 459.42
23.71 60.23 1009.76 90.67 439.66
14.39 44.84 1023.55 91.14 464.15
19.3 56.65 1020.55 70.43 459.1
24.65 52.36 1014.76 66.63 455.68
13.5 45.51 1015.33 86.95 469.08
9.82 41.26 1007.71 96.69 478.02
18.4 44.06 1017.36 70.88 456.8
28.12 44.89 1009.18 47.14 441.13
17.15 43.69 1017.05 63.36 463.88
30.69 73.67 1006.14 60.58 430.45
28.82 65.71 1014.24 54.3 449.18
21.3 48.92 1010.92 65.09 447.89
30.58 70.04 1010.4 48.16 431.59
21.17 52.3 1009.36 81.51 447.5
9.87 41.82 1033.04 68.57 475.58
22.18 59.8 1016.77 73.16 453.24
24.39 63.21 1012.59 80.88 446.4
10.73 44.92 1025.1 85.4 476.81
9.38 40.46 1019.29 75.77 474.1
20.27 57.76 1016.66 75.76 450.71
24.82 66.48 1006.4 70.21 433.62
16.55 41.66 1011.45 55.53 465.14
20.73 59.87 1019.08 80.48 445.18
9.51 39.22 1015.3 72.41 474.12
8.63 43.79 1016.08 83.25 483.91
6.48 40.27 1010.55 82.12 486.68
14.95 43.52 1022.43 94.75 464.98
5.76 45.87 1010.83 95.79 481.4
10.94 39.04 1021.81 86.02 479.2
15.87 41.16 1005.85 78.29 463.86
12.42 38.25 1012.76 82.23 472.3
29.12 58.84 1001.31 52.86 446.51
29.12 51.43 1005.93 60.66 437.71
19.08 41.1 1001.96 62.77 458.94
31.06 67.17 1007.62 65.54 437.91
5.72 39.33 1009.96 95.4 490.76
26.52 65.06 1013.4 51.78 439.66
13.84 44.9 1007.58 63.62 463.27
13.03 39.52 1016.68 83.09 473.99
25.94 66.49 1012.83 61.81 433.38
16.64 53.82 1015.13 68.24 459.01
14.13 40.75 1016.05 72.41 471.44
13.65 39.28 1012.97 79.64 471.91
14.5 44.47 1028.2 66.95 465.15
19.8 51.19 1008.25 91.98 446.66
25.2 63.76 1009.78 64.96 438.15
20.66 51.19 1008.81 88.93 447.14
12.07 43.71 1025.53 85.62 472.32
25.64 70.72 1010.16 84.0 441.68
23.33 72.99 1009.33 89.41 440.04
29.41 64.05 1009.82 67.4 444.82
16.6 53.16 1014.5 76.75 457.26
27.53 72.58 1009.13 89.06 428.83
20.62 43.43 1009.93 64.02 449.07
26.02 71.94 1009.38 64.12 435.21
12.75 44.2 1017.59 81.22 471.03
12.87 48.04 1012.47 100.13 465.56
25.77 62.96 1019.86 58.07 442.83
14.84 41.48 1017.26 63.42 460.3
7.41 40.71 1023.07 83.32 474.25
8.87 41.82 1033.3 74.28 477.97
9.69 40.46 1019.1 71.91 472.16
16.17 46.97 1014.22 85.8 456.08
26.24 49.82 1014.9 55.58 452.41
13.78 43.22 1011.31 69.7 463.71
26.3 67.07 1006.26 63.79 433.72
17.37 57.76 1016.0 86.59 456.4
23.6 48.98 1015.41 48.28 448.43
8.3 36.08 1020.63 80.42 481.6
18.86 42.18 1001.16 98.58 457.07
22.12 49.39 1019.8 72.83 451.0
28.41 75.6 1018.48 56.07 440.28
29.42 71.32 1002.26 67.13 437.47
18.61 67.71 1004.07 84.49 443.57
27.57 69.84 1004.91 68.37 426.6
12.83 41.5 1013.12 86.07 470.87
9.64 39.85 1012.9 83.82 478.37
19.13 58.66 1013.32 74.86 453.92
15.92 40.56 1020.79 53.52 470.22
24.64 72.24 1011.37 80.61 434.54
27.62 63.9 1013.11 43.56 442.89
8.9 36.24 1013.29 89.35 479.03
9.55 43.99 1020.5 97.28 476.06
10.57 36.71 1022.62 80.49 473.88
19.8 57.25 1010.84 88.9 451.75
25.63 56.85 1012.68 49.7 439.2
24.7 58.46 1015.58 68.64 439.7
15.26 46.18 1013.68 98.58 463.6
20.06 52.84 1004.21 82.12 447.47
19.84 56.89 1013.23 78.32 447.92
11.49 44.63 1020.44 86.04 471.08
23.74 72.43 1007.99 91.36 437.55
22.62 51.3 1012.36 81.02 448.27
29.53 72.39 998.47 76.05 431.69
21.32 48.14 1016.57 71.81 449.09
20.3 58.46 1015.93 82.13 448.79
16.97 44.92 1025.21 74.27 460.21
12.07 41.17 1013.54 71.32 479.28
7.46 41.82 1032.67 74.59 483.11
19.2 54.2 1011.46 84.44 450.75
28.64 66.54 1010.43 43.39 437.97
13.56 41.48 1008.53 87.2 459.76
17.4 44.9 1020.5 77.11 457.75
14.08 40.1 1015.48 82.81 469.33
27.11 69.75 1009.74 85.67 433.28
20.92 70.02 1010.23 95.58 444.64
16.18 44.9 1021.3 74.46 463.1
15.57 44.68 1022.01 90.02 460.91
10.37 39.04 1023.95 81.93 479.35
19.6 59.21 1017.65 86.29 449.23
9.22 40.92 1021.83 85.43 474.51
27.76 72.99 1007.81 71.66 435.02
28.68 70.72 1009.43 71.33 435.45
20.95 48.14 1013.3 67.72 452.38
9.06 39.3 1019.73 84.23 480.41
9.21 39.72 1019.54 74.44 478.96
13.65 42.74 1026.58 71.48 468.87
31.79 76.2 1007.89 56.3 434.01
14.32 44.6 1013.85 68.13 466.36
26.28 75.23 1011.44 68.35 435.28
7.69 43.02 1014.51 85.23 486.46
14.44 40.1 1015.51 79.78 468.19
9.19 41.01 1022.14 98.98 468.37
13.35 41.39 1019.17 72.87 474.19
23.04 74.22 1009.52 90.93 440.32
4.83 38.44 1015.35 72.94 485.32
17.29 42.86 1014.38 72.3 464.27
8.73 36.18 1013.66 77.74 479.25
26.21 70.32 1007.0 78.29 430.4
23.72 58.62 1016.65 69.1 447.49
29.27 64.69 1006.85 55.79 438.23
10.4 40.43 1025.46 75.09 492.09
12.19 40.75 1015.13 88.98 475.36
20.4 54.9 1016.68 64.26 452.56
34.3 74.67 1015.98 25.89 427.84
27.56 68.08 1010.8 59.18 433.95
30.9 70.8 1008.48 67.48 435.27
14.85 58.59 1014.04 89.85 454.62
16.42 40.56 1020.36 50.62 472.17
16.45 63.31 1015.96 83.97 452.42
10.14 42.02 1003.19 96.51 472.17
9.53 41.44 1018.01 80.09 481.83
17.01 49.15 1021.83 84.02 458.78
23.94 62.08 1022.47 61.97 447.5
15.95 49.25 1019.04 88.51 463.4
11.15 41.26 1022.67 81.83 473.57
25.56 70.32 1009.07 90.63 433.72
27.16 66.44 1011.2 73.37 431.85
26.71 77.95 1012.13 77.5 433.47
29.56 74.22 1007.45 57.46 432.84
31.19 70.94 1007.29 51.91 436.6
6.86 41.17 1020.12 79.14 490.23
12.36 41.74 1020.58 69.24 477.16
32.82 68.31 1010.44 41.85 441.06
25.3 70.98 1007.22 95.1 440.86
8.71 41.82 1033.08 74.53 477.94
13.34 40.8 1026.56 64.85 474.47
14.2 43.02 1012.18 57.07 470.67
23.74 65.34 1013.7 62.9 447.31
16.9 44.88 1018.14 72.21 466.8
28.54 71.94 1007.4 65.99 430.91
30.15 69.88 1007.2 73.67 434.75
14.33 42.86 1010.82 88.59 469.52
25.57 59.43 1008.88 61.19 438.9
30.55 70.04 1010.51 49.37 429.56
28.04 74.33 1013.53 48.65 432.92
26.39 49.16 1005.68 56.18 442.87
15.3 41.76 1022.57 71.56 466.59
6.03 41.14 1028.04 87.46 479.61
13.49 44.63 1019.12 70.02 471.08
27.67 59.14 1016.51 61.2 433.37
24.19 65.48 1018.8 60.54 443.92
24.44 59.14 1016.74 71.82 443.5
29.86 64.79 1017.37 44.8 439.89
30.2 69.59 1008.9 67.32 434.66
7.99 41.38 1021.95 78.77 487.57
9.93 41.62 1013.76 96.02 464.64
11.03 42.32 1017.26 90.56 470.92
22.34 63.73 1014.37 83.19 444.39
25.33 48.6 1002.54 68.45 442.48
18.87 52.08 1005.25 99.19 449.61
25.97 69.34 1009.43 88.11 435.02
16.58 43.99 1021.81 79.29 458.67
14.35 46.18 1016.63 87.76 461.74
25.06 62.39 1008.09 82.56 438.31
13.85 48.92 1011.68 79.24 462.38
16.09 44.2 1019.39 67.24 460.56
26.34 59.21 1013.37 58.98 439.22
23.01 58.79 1009.71 84.22 444.64
26.39 71.25 999.8 89.12 430.34
31.32 71.29 1008.37 50.07 430.46
16.64 45.87 1009.02 98.86 456.79
13.42 41.23 994.17 95.79 468.82
20.06 44.9 1008.79 70.06 448.51
14.8 44.71 1014.67 41.71 470.77
12.59 41.14 1025.79 86.55 465.74
26.7 66.56 1005.31 71.97 430.21
19.78 50.32 1008.62 96.4 449.23
15.17 49.15 1021.91 91.73 461.89
21.71 61.45 1010.97 91.62 445.72
19.09 39.39 1013.36 59.14 466.13
19.76 51.19 1008.38 92.56 448.71
14.68 41.23 998.43 83.71 469.25
21.3 66.86 1013.04 55.43 450.56
16.73 39.64 1008.94 74.91 464.46
12.26 41.5 1014.87 89.41 471.13
14.77 48.06 1010.92 69.81 461.52
18.26 59.15 1012.04 86.01 451.09
27.1 79.74 1005.43 86.05 431.51
14.72 40.83 1009.65 80.98 469.8
26.3 51.43 1012.05 63.62 442.28
16.48 48.92 1011.84 64.16 458.67
17.99 43.79 1016.13 75.63 462.4
20.34 59.8 1015.18 80.21 453.54
25.53 62.96 1019.81 59.7 444.38
31.59 58.9 1003.39 47.6 440.52
30.8 69.14 1007.68 63.78 433.62
10.75 45.0 1023.68 89.37 481.96
19.3 44.9 1008.89 70.55 452.75
4.71 39.42 1026.4 84.42 481.28
23.1 66.05 1020.28 80.62 439.03
32.63 73.88 1005.64 52.56 435.75
26.63 74.16 1009.72 83.26 436.03
24.35 58.49 1011.03 70.64 445.6
15.11 56.03 1020.27 89.95 462.65
29.1 50.05 1005.87 51.53 438.66
21.24 50.32 1008.54 84.83 447.32
6.16 39.48 1004.85 59.68 484.55
7.36 41.01 1024.9 97.88 476.8
10.44 39.04 1023.99 85.03 480.34
26.76 48.41 1010.53 47.38 440.63
16.79 44.6 1014.27 48.08 459.48
10.76 40.43 1025.98 79.65 490.78
6.07 38.91 1019.25 83.39 483.56
27.33 73.18 1012.26 82.18 429.38
27.15 59.21 1013.49 51.71 440.27
22.35 51.43 1011.34 77.33 445.34
21.82 65.27 1013.86 72.81 447.43
21.11 69.94 1004.37 84.26 439.91
19.95 50.59 1016.11 73.23 459.27
7.45 39.61 1017.88 79.73 478.89
15.36 41.66 1012.41 62.32 466.7
15.65 43.5 1021.39 78.58 463.5
25.31 74.33 1015.04 79.88 436.21
25.88 63.47 1011.95 65.87 443.94
24.6 63.94 1012.87 80.28 439.63
22.58 41.54 1013.21 71.33 460.95
19.69 59.14 1015.99 70.33 448.69
25.85 75.08 1006.24 57.73 444.63
10.06 37.83 1005.49 99.46 473.51
18.59 39.54 1008.56 68.61 462.56
18.27 50.16 1011.07 95.91 451.76
8.85 40.43 1025.68 80.42 491.81
30.04 68.08 1011.04 51.01 429.52
26.06 49.02 1007.59 74.08 437.9
14.8 38.73 1003.18 80.73 467.54
23.93 64.45 1015.35 54.71 449.97
23.72 66.48 1003.61 73.75 436.62
11.44 40.55 1023.37 88.43 477.68
20.28 63.86 1016.04 74.66 447.26
27.9 63.13 1011.8 70.04 439.76
24.74 59.39 1015.23 74.64 437.49
14.8 58.2 1018.29 85.11 455.14
8.22 41.03 1021.76 82.97 485.5
27.56 66.93 1016.81 55.59 444.1
32.07 70.94 1006.91 49.9 432.33
9.53 44.03 1008.87 89.99 471.23
13.61 42.34 1017.93 91.61 463.89
22.2 51.19 1009.2 82.95 445.54
21.36 59.54 1007.99 92.62 446.09
23.25 63.86 1017.82 59.64 445.12
23.5 59.21 1018.29 63.0 443.31
8.46 39.66 1015.14 85.38 484.16
8.19 40.69 1019.86 85.23 477.76
30.67 71.29 1008.36 52.08 430.28
32.48 62.04 1010.39 38.05 446.48
8.99 36.66 1028.11 71.98 481.03
13.77 47.83 1007.41 90.66 466.07
19.05 67.32 1013.2 83.14 447.47
21.19 55.5 1019.83 65.22 455.93
10.12 40.0 1021.15 91.67 479.62
24.93 47.01 1014.28 66.04 455.06
8.47 40.46 1019.87 78.19 475.06
24.52 56.85 1012.59 54.47 438.89
28.55 69.84 1003.38 67.26 432.7
20.58 50.9 1011.89 72.56 452.6
18.31 46.21 1010.46 82.15 451.75
27.18 71.06 1008.16 86.32 430.66
4.43 38.91 1019.04 88.17 491.9
26.02 74.78 1010.04 72.78 439.82
15.75 39.0 1015.91 69.58 460.73
22.99 60.95 1015.14 69.86 449.7
25.52 59.15 1013.88 65.37 439.42
27.04 65.06 1013.33 52.37 439.84
6.42 35.57 1025.58 79.63 485.86
17.04 40.12 1011.81 83.14 458.1
10.79 39.82 1012.89 88.25 479.92
20.41 56.03 1019.94 55.85 458.29
7.36 40.07 1017.29 52.55 489.45
28.08 73.42 1012.17 62.74 434.0
24.74 69.13 1010.69 90.08 431.24
28.32 47.93 1003.26 54.5 439.5
16.71 40.56 1019.48 49.88 467.46
30.7 71.58 1010.0 48.96 429.27
18.42 58.95 1016.95 86.77 452.1
10.62 42.02 999.83 96.66 472.41
22.18 69.05 1002.75 70.84 442.14
22.38 49.3 1003.56 83.83 441.0
13.94 41.58 1020.76 68.22 463.07
21.24 60.84 1017.99 82.22 445.71
6.76 39.81 1017.11 87.9 483.16
26.73 68.84 1010.75 66.83 440.45
7.24 38.06 1020.6 85.36 481.83
10.84 40.62 1015.53 60.9 467.6
19.32 52.84 1004.29 83.51 450.88
29.0 69.13 1001.22 52.96 425.5
23.38 54.42 1013.95 73.02 451.87
31.17 69.51 1010.51 43.11 428.94
26.17 48.6 1002.59 61.41 439.86
30.9 73.42 1011.21 65.32 433.44
24.92 73.68 1015.12 93.68 438.23
32.77 71.32 1007.68 42.39 436.95
14.37 40.56 1021.67 68.18 470.19
8.36 40.22 1011.6 89.18 484.66
31.45 68.27 1007.56 64.79 430.81
31.6 73.17 1010.05 43.48 433.37
17.9 48.98 1014.17 80.4 453.02
20.35 50.9 1012.6 72.43 453.5
16.21 41.23 995.88 80.0 463.09
19.36 44.6 1016.25 45.65 464.56
21.04 65.46 1017.22 63.02 452.12
14.05 40.69 1015.66 74.39 470.9
23.48 64.15 1021.08 57.77 450.89
21.91 63.76 1009.85 76.8 445.04
24.42 63.07 1011.49 67.39 444.72
14.26 40.92 1022.07 73.96 460.38
21.38 58.33 1013.05 72.75 446.8
15.71 44.06 1018.34 71.69 465.05
5.78 40.62 1016.55 84.98 484.13
6.77 39.81 1017.01 87.68 488.27
23.84 49.21 1013.85 50.36 447.09
21.17 58.16 1017.16 68.11 452.02
19.94 58.96 1014.16 66.27 455.55
8.73 41.92 1029.41 89.72 480.99
16.39 41.67 1012.96 61.07 467.68
col_name data_type comment
AT double null
V double null
AP double null
RH double null
PE double null
summary AT V AP RH PE
count 9568 9568 9568 9568 9568
mean 19.65123118729102 54.30580372073601 1013.2590781772603 73.30897784280926 454.3650094063554
stddev 7.4524732296110825 12.707892998326784 5.938783705811581 14.600268756728964 17.066994999803402
min 1.81 25.36 992.89 25.56 420.26
max 37.11 81.56 1033.3 100.16 495.76
Temperature Power
14.96 463.26
25.18 444.37
5.11 488.56
20.86 446.48
10.82 473.9
26.27 443.67
15.89 467.35
9.48 478.42
14.64 475.98
11.74 477.5
17.99 453.02
20.14 453.99
24.34 440.29
25.71 451.28
26.19 433.99
21.42 462.19
18.21 467.54
11.04 477.2
14.45 459.85
13.97 464.3
17.76 468.27
5.41 495.24
7.76 483.8
27.23 443.61
27.36 436.06
27.47 443.25
14.6 464.16
7.91 475.52
5.81 484.41
30.53 437.89
23.87 445.11
26.09 438.86
29.27 440.98
27.38 436.65
24.81 444.26
12.75 465.86
24.66 444.37
16.38 450.69
13.91 469.02
23.18 448.86
22.47 447.14
13.39 469.18
9.28 482.8
11.82 476.7
10.27 474.99
22.92 444.22
16.0 461.33
21.22 448.06
13.46 474.6
9.39 473.05
31.07 432.06
12.82 467.41
32.57 430.12
8.11 473.62
13.92 471.81
23.04 442.99
27.31 442.77
5.91 491.49
25.26 447.46
27.97 446.11
26.08 442.44
29.01 446.22
12.18 471.49
13.76 463.5
25.5 440.01
28.26 441.03
21.39 452.68
7.26 474.91
10.54 478.77
27.71 434.2
23.11 437.91
7.51 477.61
26.46 431.65
29.34 430.57
10.32 481.09
22.74 445.56
13.48 475.74
25.52 435.12
21.58 446.15
27.66 436.64
26.96 436.69
12.29 468.75
15.86 466.6
13.87 465.48
24.09 441.34
20.45 441.83
15.07 464.7
32.72 437.99
18.23 459.12
35.56 429.69
18.36 459.8
26.35 433.63
25.92 442.84
8.01 485.13
19.63 459.12
20.02 445.31
10.08 480.8
27.23 432.55
23.37 443.86
18.74 449.77
14.81 470.71
23.1 452.17
10.72 478.29
29.46 428.54
8.1 478.27
27.29 439.58
17.1 457.32
11.49 475.51
23.69 439.66
13.51 471.99
9.64 479.81
25.65 434.78
21.59 446.58
27.98 437.76
18.8 459.36
18.28 462.28
13.55 464.33
22.99 444.36
23.94 438.64
13.74 470.49
21.3 455.13
27.54 450.22
24.81 440.43
4.97 482.98
15.22 460.44
23.88 444.97
33.01 433.94
25.98 439.73
28.18 434.48
21.67 442.33
17.67 457.67
21.37 454.66
28.69 432.21
16.61 457.66
27.91 435.21
20.97 448.22
10.8 475.51
20.61 446.53
25.45 441.3
30.16 433.54
4.99 472.52
10.51 474.77
33.79 435.1
21.34 450.74
23.4 442.7
32.21 426.56
14.26 463.71
27.71 447.06
21.95 452.27
25.76 445.78
23.68 438.65
8.28 480.15
23.44 447.19
25.32 443.04
3.94 488.81
17.3 455.75
18.2 455.86
21.43 457.68
11.16 479.11
30.38 432.84
23.36 448.37
21.69 447.06
23.62 443.53
21.87 445.21
29.25 441.7
20.03 450.93
18.14 451.44
24.23 441.29
18.11 458.85
6.57 481.46
12.56 467.19
13.4 461.54
27.1 439.08
14.28 467.22
16.29 468.8
31.24 426.93
10.57 474.65
13.8 468.97
25.3 433.97
18.06 450.53
25.42 444.51
15.07 469.03
11.75 466.56
20.23 457.57
27.31 440.13
28.57 433.24
17.9 452.55
23.83 443.29
27.92 431.76
17.34 454.97
17.94 456.7
6.4 486.03
11.78 472.79
20.28 452.03
21.04 443.41
25.11 441.93
30.28 432.64
8.14 480.25
16.86 466.68
6.25 494.39
22.35 454.72
17.98 448.71
21.19 469.76
20.94 450.71
24.23 444.01
19.18 453.2
20.88 450.87
23.67 441.73
14.12 465.09
25.23 447.28
6.54 491.16
20.08 450.98
24.67 446.3
27.82 436.48
15.55 460.84
24.26 442.56
13.45 467.3
11.06 479.13
24.91 441.15
22.39 445.52
11.95 475.4
14.85 469.3
10.11 463.57
23.67 445.32
16.14 461.03
15.11 466.74
24.14 444.04
30.08 434.01
14.77 465.23
27.6 440.6
13.89 466.74
26.85 433.48
12.41 473.59
13.08 474.81
18.93 454.75
20.5 452.94
30.72 435.83
7.55 482.19
13.49 466.66
15.62 462.59
24.8 447.82
10.03 462.73
22.43 447.98
14.95 462.72
24.78 442.42
23.2 444.69
14.01 466.7
19.4 453.84
30.15 436.92
6.91 486.37
29.04 440.43
26.02 446.82
5.89 484.91
26.52 437.76
28.53 438.91
16.59 464.19
22.95 442.19
23.96 446.86
17.48 457.15
6.69 482.57
10.25 476.03
28.87 428.89
12.04 472.7
22.58 445.6
15.12 464.78
25.48 440.42
27.87 428.41
23.72 438.5
25.0 438.28
8.42 476.29
22.46 448.46
29.92 438.99
11.68 471.8
14.04 471.81
19.86 449.82
25.99 442.14
23.42 441.46
10.6 477.62
20.97 446.76
14.14 472.52
8.56 471.58
24.86 440.85
29.0 431.37
27.59 437.33
10.45 469.22
8.51 471.11
29.82 439.17
22.56 445.33
11.38 473.71
20.25 452.66
22.42 440.99
14.85 467.42
25.62 444.14
19.85 457.17
13.67 467.87
24.39 442.04
16.07 471.36
11.6 460.7
31.38 431.33
29.91 432.6
19.67 447.61
27.18 443.87
21.39 446.87
10.45 465.74
19.46 447.86
23.55 447.65
23.35 437.87
9.26 483.51
10.3 479.65
20.94 455.16
23.13 431.91
12.77 470.68
28.29 429.28
19.13 450.81
24.44 437.73
20.32 460.21
20.54 442.86
12.16 482.99
28.09 440.0
9.25 478.48
21.75 455.28
23.7 436.94
16.22 461.06
24.75 438.28
10.48 472.61
29.53 426.85
12.59 470.18
23.5 455.38
29.01 428.32
9.75 480.35
19.55 455.56
21.05 447.66
24.72 443.06
21.19 452.43
10.77 477.81
28.68 431.66
29.87 431.8
22.99 446.67
24.66 445.26
32.63 425.72
31.38 430.58
23.87 439.86
25.6 441.11
27.62 434.72
30.1 434.01
12.19 475.64
13.11 460.44
28.29 436.4
13.45 461.03
10.98 479.08
26.48 435.76
13.07 460.14
25.56 442.2
22.68 447.69
28.86 431.15
22.7 445.0
27.89 431.59
13.78 467.22
28.14 445.33
11.8 470.57
10.71 473.77
24.54 447.67
11.54 474.29
29.47 437.14
29.24 432.56
14.51 459.14
22.91 446.19
27.02 428.1
13.49 468.46
30.24 435.02
23.19 445.52
17.73 462.69
18.62 455.75
12.85 463.74
32.33 439.79
25.09 443.26
29.45 432.04
16.91 465.86
14.09 465.6
10.73 469.43
23.2 440.75
8.21 481.32
9.3 479.87
16.97 458.59
23.69 438.62
25.13 445.59
9.86 481.87
11.33 475.01
26.95 436.54
15.0 456.63
20.76 451.69
14.29 463.04
19.74 446.1
26.68 438.67
14.24 466.88
21.98 444.6
22.75 440.26
8.34 483.92
11.8 475.19
8.81 479.24
30.05 434.92
16.01 454.16
21.75 447.58
13.94 467.9
29.25 426.29
22.33 447.02
16.43 455.85
11.5 476.46
23.53 437.48
21.86 452.77
6.17 491.54
30.19 438.41
11.67 476.1
15.34 464.58
11.5 467.74
25.53 442.12
21.27 453.34
28.37 425.29
28.39 449.63
13.78 462.88
14.6 464.67
5.1 489.96
7.0 482.38
26.3 437.95
30.56 429.2
21.09 453.34
28.21 442.47
15.84 462.6
10.03 478.79
20.37 456.11
21.19 450.33
33.73 434.83
29.87 433.43
19.62 456.02
9.93 485.23
9.43 473.57
14.24 469.94
12.97 452.07
7.6 475.32
8.39 480.69
25.41 444.01
18.43 465.17
10.31 480.61
11.29 476.04
22.61 441.76
29.34 428.24
18.87 444.77
13.21 463.1
11.3 470.5
29.23 431.0
27.76 430.68
29.26 436.42
25.72 452.33
23.43 440.16
25.6 435.75
22.3 449.74
27.91 430.73
30.35 432.75
21.78 446.79
7.19 486.35
20.88 453.18
24.19 458.31
9.98 480.26
23.47 448.65
26.35 458.41
29.89 435.39
19.29 450.21
17.48 459.59
25.21 445.84
23.3 441.08
15.42 467.33
21.44 444.19
29.45 432.96
29.69 438.09
15.52 467.9
11.47 475.72
9.77 477.51
22.6 435.13
8.24 477.9
17.01 457.26
19.64 467.53
10.61 465.15
12.04 474.28
29.19 444.49
21.75 452.84
23.66 435.38
27.05 433.57
29.63 435.27
18.2 468.49
32.22 433.07
26.88 430.63
29.05 440.74
8.9 474.49
18.93 449.74
27.49 436.73
23.1 434.58
11.22 473.93
31.97 435.99
13.32 466.83
31.68 427.22
23.69 444.07
13.83 469.57
18.32 459.89
11.05 479.59
22.03 440.92
10.23 480.87
23.92 441.9
29.38 430.2
17.35 465.16
9.81 471.32
4.97 485.43
5.15 495.35
21.54 449.12
7.94 480.53
18.77 457.07
21.69 443.67
10.07 477.52
13.83 472.95
10.45 472.54
11.56 469.17
23.64 435.21
10.48 477.78
13.09 475.89
10.67 483.9
12.57 476.2
14.45 462.16
14.22 471.05
6.97 484.71
20.61 446.34
14.67 469.02
29.06 432.12
14.38 467.28
32.51 429.66
11.79 469.49
8.65 485.87
9.75 481.95
9.11 479.03
23.39 434.5
14.3 464.9
17.49 452.71
31.1 429.74
19.77 457.09
28.61 446.77
13.52 460.76
13.52 471.95
17.57 453.29
28.18 441.61
14.29 464.73
18.12 464.68
31.27 430.59
26.24 438.01
7.44 479.08
29.78 436.39
23.37 447.07
10.62 479.91
5.84 489.05
14.51 463.17
11.31 471.26
11.25 480.49
9.18 473.78
19.82 455.5
24.77 446.27
9.66 482.2
21.96 452.48
18.59 464.48
24.75 438.1
24.37 445.6
29.6 442.43
25.32 436.67
16.15 466.56
15.74 457.29
5.97 487.03
15.84 464.93
14.84 466.0
12.25 469.52
27.38 428.88
8.76 474.3
15.54 461.06
18.71 465.57
13.06 467.67
12.72 466.99
19.83 463.72
27.23 443.78
24.27 445.23
11.8 464.43
6.76 484.36
25.99 442.16
16.3 464.11
16.5 462.48
10.59 477.49
26.05 437.04
19.5 457.09
22.21 450.6
17.86 465.78
29.96 427.1
19.08 459.81
23.59 447.36
3.38 488.92
26.39 433.36
8.99 483.35
10.91 469.53
13.08 476.96
23.95 440.75
15.64 462.55
18.78 448.04
20.65 455.24
4.96 494.75
23.51 444.58
5.99 484.82
23.65 442.9
5.17 485.46
26.38 457.81
6.02 481.92
23.2 443.23
8.57 474.29
30.72 430.46
21.52 455.71
22.93 438.34
5.71 485.83
18.62 452.82
27.88 435.04
22.32 451.21
14.55 465.81
17.83 458.42
9.68 470.22
19.41 449.24
13.22 471.43
12.24 473.26
19.21 452.82
29.74 432.69
23.28 444.13
8.02 467.21
22.47 445.98
27.51 436.91
17.51 455.01
23.22 437.11
11.73 477.06
21.19 441.71
5.48 495.76
24.26 445.63
12.32 464.72
31.26 438.03
32.09 434.78
24.98 444.67
27.48 452.24
21.04 450.92
27.75 436.53
22.79 435.53
24.22 440.01
27.06 443.1
29.25 427.49
26.86 436.25
29.64 440.74
19.92 443.54
18.5 459.42
23.71 439.66
14.39 464.15
19.3 459.1
24.65 455.68
13.5 469.08
9.82 478.02
18.4 456.8
28.12 441.13
17.15 463.88
30.69 430.45
28.82 449.18
21.3 447.89
30.58 431.59
21.17 447.5
9.87 475.58
22.18 453.24
24.39 446.4
10.73 476.81
9.38 474.1
20.27 450.71
24.82 433.62
16.55 465.14
20.73 445.18
9.51 474.12
8.63 483.91
6.48 486.68
14.95 464.98
5.76 481.4
10.94 479.2
15.87 463.86
12.42 472.3
29.12 446.51
29.12 437.71
19.08 458.94
31.06 437.91
5.72 490.76
26.52 439.66
13.84 463.27
13.03 473.99
25.94 433.38
16.64 459.01
14.13 471.44
13.65 471.91
14.5 465.15
19.8 446.66
25.2 438.15
20.66 447.14
12.07 472.32
25.64 441.68
23.33 440.04
29.41 444.82
16.6 457.26
27.53 428.83
20.62 449.07
26.02 435.21
12.75 471.03
12.87 465.56
25.77 442.83
14.84 460.3
7.41 474.25
8.87 477.97
9.69 472.16
16.17 456.08
26.24 452.41
13.78 463.71
26.3 433.72
17.37 456.4
23.6 448.43
8.3 481.6
18.86 457.07
22.12 451.0
28.41 440.28
29.42 437.47
18.61 443.57
27.57 426.6
12.83 470.87
9.64 478.37
19.13 453.92
15.92 470.22
24.64 434.54
27.62 442.89
8.9 479.03
9.55 476.06
10.57 473.88
19.8 451.75
25.63 439.2
24.7 439.7
15.26 463.6
20.06 447.47
19.84 447.92
11.49 471.08
23.74 437.55
22.62 448.27
29.53 431.69
21.32 449.09
20.3 448.79
16.97 460.21
12.07 479.28
7.46 483.11
19.2 450.75
28.64 437.97
13.56 459.76
17.4 457.75
14.08 469.33
27.11 433.28
20.92 444.64
16.18 463.1
15.57 460.91
10.37 479.35
19.6 449.23
9.22 474.51
27.76 435.02
28.68 435.45
20.95 452.38
9.06 480.41
9.21 478.96
13.65 468.87
31.79 434.01
14.32 466.36
26.28 435.28
7.69 486.46
14.44 468.19
9.19 468.37
13.35 474.19
23.04 440.32
4.83 485.32
17.29 464.27
8.73 479.25
26.21 430.4
23.72 447.49
29.27 438.23
10.4 492.09
12.19 475.36
20.4 452.56
34.3 427.84
27.56 433.95
30.9 435.27
14.85 454.62
16.42 472.17
16.45 452.42
10.14 472.17
9.53 481.83
17.01 458.78
23.94 447.5
15.95 463.4
11.15 473.57
25.56 433.72
27.16 431.85
26.71 433.47
29.56 432.84
31.19 436.6
6.86 490.23
12.36 477.16
32.82 441.06
25.3 440.86
8.71 477.94
13.34 474.47
14.2 470.67
23.74 447.31
16.9 466.8
28.54 430.91
30.15 434.75
14.33 469.52
25.57 438.9
30.55 429.56
28.04 432.92
26.39 442.87
15.3 466.59
6.03 479.61
13.49 471.08
27.67 433.37
24.19 443.92
24.44 443.5
29.86 439.89
30.2 434.66
7.99 487.57
9.93 464.64
11.03 470.92
22.34 444.39
25.33 442.48
18.87 449.61
25.97 435.02
16.58 458.67
14.35 461.74
25.06 438.31
13.85 462.38
16.09 460.56
26.34 439.22
23.01 444.64
26.39 430.34
31.32 430.46
16.64 456.79
13.42 468.82
20.06 448.51
14.8 470.77
12.59 465.74
26.7 430.21
19.78 449.23
15.17 461.89
21.71 445.72
19.09 466.13
19.76 448.71
14.68 469.25
21.3 450.56
16.73 464.46
12.26 471.13
14.77 461.52
18.26 451.09
27.1 431.51
14.72 469.8
26.3 442.28
16.48 458.67
17.99 462.4
20.34 453.54
25.53 444.38
31.59 440.52
30.8 433.62
10.75 481.96
19.3 452.75
4.71 481.28
23.1 439.03
32.63 435.75
26.63 436.03
24.35 445.6
15.11 462.65
29.1 438.66
21.24 447.32
6.16 484.55
7.36 476.8
10.44 480.34
26.76 440.63
16.79 459.48
10.76 490.78
6.07 483.56
27.33 429.38
27.15 440.27
22.35 445.34
21.82 447.43
21.11 439.91
19.95 459.27
7.45 478.89
15.36 466.7
15.65 463.5
25.31 436.21
25.88 443.94
24.6 439.63
22.58 460.95
19.69 448.69
25.85 444.63
10.06 473.51
18.59 462.56
18.27 451.76
8.85 491.81
30.04 429.52
26.06 437.9
14.8 467.54
23.93 449.97
23.72 436.62
11.44 477.68
20.28 447.26
27.9 439.76
24.74 437.49
14.8 455.14
8.22 485.5
27.56 444.1
32.07 432.33
9.53 471.23
13.61 463.89
22.2 445.54
21.36 446.09
23.25 445.12
23.5 443.31
8.46 484.16
8.19 477.76
30.67 430.28
32.48 446.48
8.99 481.03
13.77 466.07
19.05 447.47
21.19 455.93
10.12 479.62
24.93 455.06
8.47 475.06
24.52 438.89
28.55 432.7
20.58 452.6
18.31 451.75
27.18 430.66
4.43 491.9
26.02 439.82
15.75 460.73
22.99 449.7
25.52 439.42
27.04 439.84
6.42 485.86
17.04 458.1
10.79 479.92
20.41 458.29
7.36 489.45
28.08 434.0
24.74 431.24
28.32 439.5
16.71 467.46
30.7 429.27
18.42 452.1
10.62 472.41
22.18 442.14
22.38 441.0
13.94 463.07
21.24 445.71
6.76 483.16
26.73 440.45
7.24 481.83
10.84 467.6
19.32 450.88
29.0 425.5
23.38 451.87
31.17 428.94
26.17 439.86
30.9 433.44
24.92 438.23
32.77 436.95
14.37 470.19
8.36 484.66
31.45 430.81
31.6 433.37
17.9 453.02
20.35 453.5
16.21 463.09
19.36 464.56
21.04 452.12
14.05 470.9
23.48 450.89
21.91 445.04
24.42 444.72
14.26 460.38
21.38 446.8
15.71 465.05
5.78 484.13
6.77 488.27
23.84 447.09
21.17 452.02
19.94 455.55
8.73 480.99
16.39 467.68
ExhaustVaccum Power
41.76 463.26
62.96 444.37
39.4 488.56
57.32 446.48
37.5 473.9
59.44 443.67
43.96 467.35
44.71 478.42
45.0 475.98
43.56 477.5
43.72 453.02
46.93 453.99
73.5 440.29
58.59 451.28
69.34 433.99
43.79 462.19
45.0 467.54
41.74 477.2
52.75 459.85
38.47 464.3
42.42 468.27
40.07 495.24
42.28 483.8
63.9 443.61
48.6 436.06
70.72 443.25
39.31 464.16
39.96 475.52
35.79 484.41
65.18 437.89
63.94 445.11
58.41 438.86
66.85 440.98
74.16 436.65
63.94 444.26
44.03 465.86
63.73 444.37
47.45 450.69
39.35 469.02
51.3 448.86
47.45 447.14
44.85 469.18
41.54 482.8
42.86 476.7
40.64 474.99
63.94 444.22
37.87 461.33
43.43 448.06
44.71 474.6
40.11 473.05
73.5 432.06
38.62 467.41
78.92 430.12
42.18 473.62
39.39 471.81
59.43 442.99
64.44 442.77
39.33 491.49
61.08 447.46
58.84 446.11
52.3 442.44
65.71 446.22
40.1 471.49
45.87 463.5
58.79 440.01
65.34 441.03
62.96 452.68
40.69 474.91
34.03 478.77
74.34 434.2
68.3 437.91
41.01 477.61
74.67 431.65
74.34 430.57
42.28 481.09
61.02 445.56
39.85 475.74
69.75 435.12
67.25 446.15
76.86 436.64
69.45 436.69
42.18 468.75
43.02 466.6
45.08 465.48
73.68 441.34
69.45 441.83
39.3 464.7
69.75 437.99
58.96 459.12
68.94 429.69
51.43 459.8
64.05 433.63
60.95 442.84
41.66 485.13
52.72 459.12
67.32 445.31
40.72 480.8
66.48 432.55
63.77 443.86
59.21 449.77
43.69 470.71
51.3 452.17
41.38 478.29
71.94 428.54
40.64 478.27
62.66 439.58
49.69 457.32
44.2 475.51
65.59 439.66
40.89 471.99
39.35 479.81
78.92 434.78
61.87 446.58
58.33 437.76
39.72 459.36
44.71 462.28
43.48 464.33
46.21 444.36
59.39 438.64
34.03 470.49
41.1 455.13
66.93 450.22
63.73 440.43
42.85 482.98
50.88 460.44
54.2 444.97
68.67 433.94
73.18 439.73
73.88 434.48
60.84 442.33
45.09 457.67
57.76 454.66
67.25 432.21
43.77 457.66
63.76 435.21
47.43 448.22
41.66 475.51
62.91 446.53
57.32 441.3
69.34 433.54
39.04 472.52
44.78 474.77
69.05 435.1
59.8 450.74
65.06 442.7
68.14 426.56
42.32 463.71
66.93 447.06
57.76 452.27
63.94 445.78
68.3 438.65
40.77 480.15
62.52 447.19
48.41 443.04
39.9 488.81
57.76 455.75
49.39 455.86
46.97 457.68
40.05 479.11
74.16 432.84
62.52 448.37
47.45 447.06
49.21 443.53
61.45 445.21
66.51 441.7
66.86 450.93
49.78 451.44
56.89 441.29
44.85 458.85
43.65 481.46
43.41 467.19
41.58 461.54
52.84 439.08
42.74 467.22
44.34 468.8
71.98 426.93
37.73 474.65
44.21 468.97
71.58 433.97
50.16 450.53
59.04 444.51
40.69 469.03
71.14 466.56
52.05 457.57
59.54 440.13
69.84 433.24
43.72 452.55
71.37 443.29
74.99 431.76
44.78 454.97
63.07 456.7
39.9 486.03
39.96 472.79
57.25 452.03
54.2 443.41
67.32 441.93
70.98 432.64
36.24 480.25
39.63 466.68
40.07 494.39
54.42 454.72
56.85 448.71
42.48 469.76
44.89 450.71
58.79 444.01
58.2 453.2
57.85 450.87
63.86 441.73
39.52 465.09
64.63 447.28
39.33 491.16
62.52 450.98
63.56 446.3
79.74 436.48
42.03 460.84
69.51 442.56
41.49 467.3
40.64 479.13
52.3 441.15
59.04 445.52
40.69 475.4
40.69 469.3
41.62 463.57
68.67 445.32
44.21 461.03
43.13 466.74
59.87 444.04
67.25 434.01
44.9 465.23
69.34 440.6
44.84 466.74
75.6 433.48
40.96 473.59
41.74 474.81
44.06 454.75
49.69 452.94
69.13 435.83
39.22 482.19
44.47 466.66
40.12 462.59
64.63 447.82
41.62 462.73
63.21 447.98
39.31 462.72
58.46 442.42
48.41 444.69
39.0 466.7
64.63 453.84
67.32 436.92
36.08 486.37
60.07 440.43
63.07 446.82
39.48 484.91
71.64 437.76
68.08 438.91
39.54 464.19
67.79 442.19
47.43 446.86
44.2 457.15
43.65 482.57
41.26 476.03
72.58 428.89
40.23 472.7
52.3 445.6
52.05 464.78
58.95 440.42
70.79 428.41
70.47 438.5
59.43 438.28
40.64 476.29
58.49 448.46
57.19 438.99
39.22 471.8
42.44 471.81
59.14 449.82
68.08 442.14
58.79 441.46
40.22 477.62
61.87 446.76
39.82 472.52
40.71 471.58
72.39 440.85
77.54 431.37
71.97 437.33
40.71 469.22
40.78 471.11
66.51 439.17
62.26 445.33
39.22 473.71
57.76 452.66
59.43 440.99
38.91 467.42
58.82 444.14
56.53 457.17
54.3 467.87
70.72 442.04
44.58 471.36
39.1 460.7
70.83 431.33
76.86 432.6
59.39 447.61
64.79 443.87
52.3 446.87
41.01 465.74
56.89 447.86
62.96 447.65
63.47 437.87
41.66 483.51
41.46 479.65
58.16 455.16
71.25 431.91
41.5 470.68
69.13 429.28
59.21 450.81
73.5 437.73
44.6 460.21
69.05 442.86
45.0 482.99
65.27 440.0
41.82 478.48
49.82 455.28
66.56 436.94
37.87 461.06
69.45 438.28
39.58 472.61
70.79 426.85
39.72 470.18
54.42 455.38
66.56 428.32
42.49 480.35
56.53 455.56
58.33 447.66
68.67 443.06
58.86 452.43
41.54 477.81
73.77 431.66
73.91 431.8
68.67 446.67
60.29 445.26
69.89 425.72
72.29 430.58
60.27 439.86
59.15 441.11
71.14 434.72
67.45 434.01
41.17 475.64
41.58 460.44
68.67 436.4
40.73 461.03
41.54 479.08
69.14 435.76
45.51 460.14
75.6 442.2
50.78 447.69
73.67 431.15
63.56 445.0
73.21 431.59
44.47 467.22
51.43 445.33
45.09 470.57
39.61 473.77
60.29 447.67
40.05 474.29
71.32 437.14
69.05 432.56
41.79 459.14
60.07 446.19
71.77 428.1
44.47 468.46
66.75 435.02
48.6 445.52
40.55 462.69
61.27 455.75
40.0 463.74
69.68 439.79
58.95 443.26
69.13 432.04
43.96 465.86
45.87 465.6
25.36 469.43
49.3 440.75
38.91 481.32
40.56 479.87
39.16 458.59
71.97 438.62
59.44 445.59
43.56 481.87
41.5 475.01
48.41 436.54
40.66 456.63
62.52 451.69
39.59 463.04
67.71 446.1
59.92 438.67
41.4 466.88
48.41 444.6
59.39 440.26
40.96 483.92
41.2 475.19
44.68 479.24
73.68 434.92
65.46 454.16
58.79 447.58
41.26 467.9
69.13 426.29
45.87 447.02
41.79 455.85
40.22 476.46
68.94 437.48
49.21 452.77
39.33 491.54
64.79 438.41
41.93 476.1
36.99 464.58
40.78 467.74
57.17 442.12
57.5 453.34
69.13 425.29
51.43 449.63
45.78 462.88
42.32 464.67
35.57 489.96
38.08 482.38
77.95 437.95
71.98 429.2
46.63 453.34
70.02 442.47
49.69 462.6
40.96 478.79
52.05 456.11
50.16 450.33
69.88 434.83
73.68 433.43
62.96 456.02
40.67 485.23
37.14 473.57
39.58 469.94
49.83 452.07
41.04 475.32
36.24 480.69
48.06 444.01
56.03 465.17
39.82 480.61
41.5 476.04
49.3 441.76
71.98 428.24
67.71 444.77
45.87 463.1
44.6 470.5
72.99 431.0
69.4 430.68
67.17 436.42
49.82 452.33
63.94 440.16
63.76 435.75
44.57 449.74
72.24 430.73
77.17 432.75
47.43 446.79
41.39 486.35
59.8 453.18
50.23 458.31
41.54 480.26
51.3 448.65
49.5 458.41
64.69 435.39
50.16 450.21
43.14 459.59
75.6 445.84
48.78 441.08
37.85 467.33
63.09 444.19
68.27 432.96
47.93 438.09
36.99 467.9
43.67 475.72
34.69 477.51
69.84 435.13
39.61 477.9
44.2 457.26
44.6 467.53
41.58 465.15
40.1 474.28
65.71 444.49
45.09 452.84
77.54 435.38
75.33 433.57
69.71 435.27
39.63 468.49
70.8 433.07
73.56 430.63
65.74 440.74
39.96 474.49
48.6 449.74
63.76 436.73
70.79 434.58
43.13 473.93
79.74 435.99
43.22 466.83
68.24 427.22
63.77 444.07
41.49 469.57
66.51 459.89
40.71 479.59
64.69 440.92
41.46 480.87
66.54 441.9
69.68 430.2
42.86 465.16
44.45 471.32
40.64 485.43
40.07 495.35
58.49 449.12
42.02 480.53
50.66 457.07
69.94 443.67
44.68 477.52
39.64 472.95
39.69 472.54
40.71 469.17
70.04 435.21
40.22 477.78
39.85 475.89
40.23 483.9
39.16 476.2
43.34 462.16
37.85 471.05
41.26 484.71
63.86 446.34
42.28 469.02
72.86 432.12
40.1 467.28
69.98 429.66
45.09 469.49
40.56 485.87
40.81 481.95
40.02 479.03
69.13 434.5
54.3 464.9
63.94 452.71
69.51 429.74
56.65 457.09
72.29 446.77
41.48 460.76
40.83 471.95
46.21 453.29
60.07 441.61
46.18 464.73
43.69 464.68
73.91 430.59
77.95 438.01
41.04 479.08
74.78 436.39
65.46 447.07
39.58 479.91
43.02 489.05
53.82 463.17
42.02 471.26
40.67 480.49
39.42 473.78
58.16 455.5
58.41 446.27
41.06 482.2
59.8 452.48
43.14 464.48
69.89 438.1
63.47 445.6
67.79 442.43
61.25 436.67
41.85 466.56
71.14 457.29
36.25 487.03
52.72 464.93
44.63 466.0
48.79 469.52
70.04 428.88
41.48 474.3
39.31 461.06
39.39 465.57
41.78 467.67
40.71 466.99
39.39 463.72
49.16 443.78
68.28 445.23
40.66 464.43
36.25 484.36
63.07 442.16
39.63 464.11
49.39 462.48
42.49 477.49
65.59 437.04
40.79 457.09
45.01 450.6
45.0 465.78
70.04 427.1
44.63 459.81
47.43 447.36
39.64 488.92
66.49 433.36
39.04 483.35
41.04 469.53
39.82 476.96
58.46 440.75
43.71 462.55
54.2 448.04
50.59 455.24
40.07 494.75
57.32 444.58
35.79 484.82
66.05 442.9
39.33 485.46
49.5 457.81
43.65 481.92
61.02 443.23
39.69 474.29
71.58 430.46
50.66 455.71
62.26 438.34
41.31 485.83
44.06 452.82
68.94 435.04
59.8 451.21
42.74 465.81
44.92 458.42
39.96 470.22
49.39 449.24
44.92 471.43
44.92 473.26
58.49 452.82
70.32 432.69
60.84 444.13
41.92 467.21
48.6 445.98
73.77 436.91
44.9 455.01
66.56 437.11
40.64 477.06
67.71 441.71
40.07 495.76
66.44 445.63
41.62 464.72
68.94 438.03
72.86 434.78
60.32 444.67
61.41 452.24
45.09 450.92
70.4 436.53
71.77 435.53
68.51 440.01
64.45 443.1
71.94 427.49
68.08 436.25
67.79 440.74
63.31 443.54
51.43 459.42
60.23 439.66
44.84 464.15
56.65 459.1
52.36 455.68
45.51 469.08
41.26 478.02
44.06 456.8
44.89 441.13
43.69 463.88
73.67 430.45
65.71 449.18
48.92 447.89
70.04 431.59
52.3 447.5
41.82 475.58
59.8 453.24
63.21 446.4
44.92 476.81
40.46 474.1
57.76 450.71
66.48 433.62
41.66 465.14
59.87 445.18
39.22 474.12
43.79 483.91
40.27 486.68
43.52 464.98
45.87 481.4
39.04 479.2
41.16 463.86
38.25 472.3
58.84 446.51
51.43 437.71
41.1 458.94
67.17 437.91
39.33 490.76
65.06 439.66
44.9 463.27
39.52 473.99
66.49 433.38
53.82 459.01
40.75 471.44
39.28 471.91
44.47 465.15
51.19 446.66
63.76 438.15
51.19 447.14
43.71 472.32
70.72 441.68
72.99 440.04
64.05 444.82
53.16 457.26
72.58 428.83
43.43 449.07
71.94 435.21
44.2 471.03
48.04 465.56
62.96 442.83
41.48 460.3
40.71 474.25
41.82 477.97
40.46 472.16
46.97 456.08
49.82 452.41
43.22 463.71
67.07 433.72
57.76 456.4
48.98 448.43
36.08 481.6
42.18 457.07
49.39 451.0
75.6 440.28
71.32 437.47
67.71 443.57
69.84 426.6
41.5 470.87
39.85 478.37
58.66 453.92
40.56 470.22
72.24 434.54
63.9 442.89
36.24 479.03
43.99 476.06
36.71 473.88
57.25 451.75
56.85 439.2
58.46 439.7
46.18 463.6
52.84 447.47
56.89 447.92
44.63 471.08
72.43 437.55
51.3 448.27
72.39 431.69
48.14 449.09
58.46 448.79
44.92 460.21
41.17 479.28
41.82 483.11
54.2 450.75
66.54 437.97
41.48 459.76
44.9 457.75
40.1 469.33
69.75 433.28
70.02 444.64
44.9 463.1
44.68 460.91
39.04 479.35
59.21 449.23
40.92 474.51
72.99 435.02
70.72 435.45
48.14 452.38
39.3 480.41
39.72 478.96
42.74 468.87
76.2 434.01
44.6 466.36
75.23 435.28
43.02 486.46
40.1 468.19
41.01 468.37
41.39 474.19
74.22 440.32
38.44 485.32
42.86 464.27
36.18 479.25
70.32 430.4
58.62 447.49
64.69 438.23
40.43 492.09
40.75 475.36
54.9 452.56
74.67 427.84
68.08 433.95
70.8 435.27
58.59 454.62
40.56 472.17
63.31 452.42
42.02 472.17
41.44 481.83
49.15 458.78
62.08 447.5
49.25 463.4
41.26 473.57
70.32 433.72
66.44 431.85
77.95 433.47
74.22 432.84
70.94 436.6
41.17 490.23
41.74 477.16
68.31 441.06
70.98 440.86
41.82 477.94
40.8 474.47
43.02 470.67
65.34 447.31
44.88 466.8
71.94 430.91
69.88 434.75
42.86 469.52
59.43 438.9
70.04 429.56
74.33 432.92
49.16 442.87
41.76 466.59
41.14 479.61
44.63 471.08
59.14 433.37
65.48 443.92
59.14 443.5
64.79 439.89
69.59 434.66
41.38 487.57
41.62 464.64
42.32 470.92
63.73 444.39
48.6 442.48
52.08 449.61
69.34 435.02
43.99 458.67
46.18 461.74
62.39 438.31
48.92 462.38
44.2 460.56
59.21 439.22
58.79 444.64
71.25 430.34
71.29 430.46
45.87 456.79
41.23 468.82
44.9 448.51
44.71 470.77
41.14 465.74
66.56 430.21
50.32 449.23
49.15 461.89
61.45 445.72
39.39 466.13
51.19 448.71
41.23 469.25
66.86 450.56
39.64 464.46
41.5 471.13
48.06 461.52
59.15 451.09
79.74 431.51
40.83 469.8
51.43 442.28
48.92 458.67
43.79 462.4
59.8 453.54
62.96 444.38
58.9 440.52
69.14 433.62
45.0 481.96
44.9 452.75
39.42 481.28
66.05 439.03
73.88 435.75
74.16 436.03
58.49 445.6
56.03 462.65
50.05 438.66
50.32 447.32
39.48 484.55
41.01 476.8
39.04 480.34
48.41 440.63
44.6 459.48
40.43 490.78
38.91 483.56
73.18 429.38
59.21 440.27
51.43 445.34
65.27 447.43
69.94 439.91
50.59 459.27
39.61 478.89
41.66 466.7
43.5 463.5
74.33 436.21
63.47 443.94
63.94 439.63
41.54 460.95
59.14 448.69
75.08 444.63
37.83 473.51
39.54 462.56
50.16 451.76
40.43 491.81
68.08 429.52
49.02 437.9
38.73 467.54
64.45 449.97
66.48 436.62
40.55 477.68
63.86 447.26
63.13 439.76
59.39 437.49
58.2 455.14
41.03 485.5
66.93 444.1
70.94 432.33
44.03 471.23
42.34 463.89
51.19 445.54
59.54 446.09
63.86 445.12
59.21 443.31
39.66 484.16
40.69 477.76
71.29 430.28
62.04 446.48
36.66 481.03
47.83 466.07
67.32 447.47
55.5 455.93
40.0 479.62
47.01 455.06
40.46 475.06
56.85 438.89
69.84 432.7
50.9 452.6
46.21 451.75
71.06 430.66
38.91 491.9
74.78 439.82
39.0 460.73
60.95 449.7
59.15 439.42
65.06 439.84
35.57 485.86
40.12 458.1
39.82 479.92
56.03 458.29
40.07 489.45
73.42 434.0
69.13 431.24
47.93 439.5
40.56 467.46
71.58 429.27
58.95 452.1
42.02 472.41
69.05 442.14
49.3 441.0
41.58 463.07
60.84 445.71
39.81 483.16
68.84 440.45
38.06 481.83
40.62 467.6
52.84 450.88
69.13 425.5
54.42 451.87
69.51 428.94
48.6 439.86
73.42 433.44
73.68 438.23
71.32 436.95
40.56 470.19
40.22 484.66
68.27 430.81
73.17 433.37
48.98 453.02
50.9 453.5
41.23 463.09
44.6 464.56
65.46 452.12
40.69 470.9
64.15 450.89
63.76 445.04
63.07 444.72
40.92 460.38
58.33 446.8
44.06 465.05
40.62 484.13
39.81 488.27
49.21 447.09
58.16 452.02
58.96 455.55
41.92 480.99
41.67 467.68
Pressure Power
1024.07 463.26
1020.04 444.37
1012.16 488.56
1010.24 446.48
1009.23 473.9
1012.23 443.67
1014.02 467.35
1019.12 478.42
1021.78 475.98
1015.14 477.5
1008.64 453.02
1014.66 453.99
1011.31 440.29
1012.77 451.28
1009.48 433.99
1015.76 462.19
1022.86 467.54
1022.6 477.2
1023.97 459.85
1015.15 464.3
1009.09 468.27
1019.16 495.24
1008.52 483.8
1014.3 443.61
1003.18 436.06
1009.97 443.25
1011.11 464.16
1023.57 475.52
1012.14 484.41
1012.69 437.89
1019.02 445.11
1013.64 438.86
1011.11 440.98
1010.08 436.65
1018.76 444.26
1007.29 465.86
1011.4 444.37
1010.08 450.69
1014.69 469.02
1012.04 448.86
1007.62 447.14
1017.24 469.18
1018.33 482.8
1014.12 476.7
1020.63 474.99
1019.28 444.22
1020.24 461.33
1010.96 448.06
1014.51 474.6
1029.14 473.05
1010.58 432.06
1018.71 467.41
1011.6 430.12
1014.82 473.62
1012.94 471.81
1010.23 442.99
1014.65 442.77
1010.18 491.49
1013.68 447.46
1002.25 446.11
1007.03 442.44
1013.61 446.22
1016.67 471.49
1008.89 463.5
1016.02 440.01
1014.56 441.03
1019.49 452.68
1020.43 474.91
1018.71 478.77
998.14 434.2
1017.83 437.91
1024.61 477.61
1016.65 431.65
998.58 430.57
1008.82 481.09
1009.56 445.56
1012.71 475.74
1010.36 435.12
1017.39 446.15
1001.31 436.64
1013.89 436.69
1016.53 468.75
1012.18 466.6
1024.42 465.48
1014.93 441.34
1012.53 441.83
1019.0 464.7
1009.6 437.99
1015.55 459.12
1006.56 429.69
1010.57 459.8
1009.81 433.63
1014.62 442.84
1014.49 485.13
1025.09 459.12
1012.05 445.31
1022.7 480.8
1005.23 432.55
1013.42 443.86
1018.3 449.77
1017.19 470.71
1011.93 452.17
1021.6 478.29
1006.96 428.54
1020.66 478.27
1007.63 439.58
1005.53 457.32
1018.79 475.51
1010.85 439.66
1011.03 471.99
1015.1 479.81
1010.83 434.78
1011.18 446.58
1013.92 437.76
1001.24 459.36
1016.99 462.28
1016.08 464.33
1010.71 444.36
1014.32 438.64
1018.69 470.49
1001.86 455.13
1017.06 450.22
1009.34 440.43
1014.02 482.98
1014.19 460.44
1012.81 444.97
1005.2 433.94
1012.28 439.73
1005.89 434.48
1017.93 442.33
1014.26 457.67
1018.8 454.66
1017.71 432.21
1012.25 457.66
1010.27 435.21
1007.64 448.22
1013.79 475.51
1013.24 446.53
1011.7 441.3
1007.67 433.54
1020.45 472.52
1012.59 474.77
1001.62 435.1
1016.92 450.74
1014.32 442.7
1003.34 426.56
1016.0 463.71
1016.85 447.06
1018.02 452.27
1018.49 445.78
1017.93 438.65
1011.55 480.15
1016.46 447.19
1008.47 443.04
1008.06 488.81
1016.26 455.75
1018.83 455.86
1013.94 457.68
1014.95 479.11
1007.44 432.84
1016.18 448.37
1007.56 447.06
1014.1 443.53
1011.13 445.21
1015.53 441.7
1013.05 450.93
1002.95 451.44
1012.32 441.29
1014.48 458.85
1018.24 481.46
1016.93 467.19
1020.5 461.54
1006.28 439.08
1028.79 467.22
1019.49 468.8
1004.66 426.93
1024.36 474.65
1022.93 468.97
1010.18 433.97
1009.52 450.53
1011.98 444.51
1015.29 469.03
1019.36 466.56
1012.15 457.57
1006.24 440.13
1003.57 433.24
1008.64 452.55
1002.04 443.29
1005.47 431.76
1007.81 454.97
1012.42 456.7
1007.75 486.03
1011.37 472.79
1010.12 452.03
1012.26 443.41
1014.49 441.93
1007.51 432.64
1013.15 480.25
1004.47 466.68
1020.19 494.39
1012.46 454.72
1012.28 448.71
1013.43 469.76
1009.64 450.71
1009.8 444.01
1017.46 453.2
1012.39 450.87
1019.67 441.73
1018.41 465.09
1020.59 447.28
1011.54 491.16
1017.99 450.98
1013.75 446.3
1008.37 436.48
1017.41 460.84
1013.43 442.56
1020.19 467.3
1021.47 479.13
1008.72 441.15
1011.78 445.52
1015.62 475.4
1014.91 469.3
1017.17 463.57
1006.71 445.32
1020.36 461.03
1014.99 466.74
1018.47 444.04
1017.6 434.01
1020.5 465.23
1009.63 440.6
1023.66 466.74
1017.43 433.48
1023.36 473.59
1020.75 474.81
1017.58 454.75
1009.6 452.94
1009.94 435.83
1014.53 482.19
1030.46 466.66
1013.03 462.59
1020.69 447.82
1014.55 462.73
1012.06 447.98
1009.15 462.72
1016.82 442.42
1008.64 444.69
1016.73 466.7
1020.38 453.84
1013.83 436.92
1021.82 486.37
1015.42 440.43
1010.94 446.82
1005.11 484.91
1008.27 437.76
1013.27 438.91
1007.97 464.19
1009.89 442.19
1008.38 446.86
1018.89 457.15
1020.14 482.57
1007.44 476.03
1008.69 428.89
1018.07 472.7
1009.04 445.6
1014.63 464.78
1017.02 440.42
1003.96 428.41
1010.65 438.5
1007.84 438.28
1022.35 476.29
1011.5 448.46
1008.62 438.99
1017.9 471.8
1012.74 471.81
1016.12 449.82
1013.13 442.14
1009.74 441.46
1011.37 477.62
1011.45 446.76
1012.46 472.52
1021.27 471.58
1001.15 440.85
1011.33 431.37
1008.64 437.33
1015.68 469.22
1023.51 471.11
1010.98 439.17
1012.11 445.33
1018.62 473.71
1016.28 452.66
1007.12 440.99
1014.48 467.42
1010.02 444.14
1020.57 457.17
1015.92 467.87
1009.78 442.04
1019.52 471.36
1009.81 460.7
1010.35 431.33
998.59 432.6
1014.07 447.61
1016.27 443.87
1009.2 446.87
1020.57 465.74
1014.02 447.86
1020.16 447.65
1011.78 437.87
1016.87 483.51
1018.21 479.65
1016.88 455.16
1002.49 431.91
1014.13 470.68
1009.29 429.28
1018.32 450.81
1011.49 437.73
1015.16 460.21
1001.6 442.86
1021.51 482.99
1013.27 440.0
1033.25 478.48
1015.01 455.28
1002.07 436.94
1022.36 461.06
1013.97 438.28
1011.81 472.61
1003.7 426.85
1017.76 470.18
1012.31 455.38
1006.44 428.32
1010.57 480.35
1020.2 455.56
1013.14 447.66
1006.74 443.06
1014.19 452.43
1019.94 477.81
1004.72 431.66
1004.53 431.8
1006.65 446.67
1018.0 445.26
1013.85 425.72
1008.73 430.58
1018.94 439.86
1013.31 441.11
1011.6 434.72
1014.23 434.01
1019.43 475.64
1020.43 460.44
1005.46 436.4
1018.7 461.03
1019.94 479.08
1009.31 435.76
1015.22 460.14
1017.37 442.2
1008.83 447.69
1006.65 431.15
1014.32 445.0
1001.32 431.59
1027.94 467.22
1012.16 445.33
1013.21 470.57
1018.72 473.77
1017.42 447.67
1014.78 474.29
1008.07 437.14
1003.12 432.56
1009.72 459.14
1016.03 446.19
1006.38 428.1
1030.18 468.46
1017.95 435.02
1002.38 445.52
1003.36 462.69
1019.26 455.75
1015.89 463.74
1011.95 439.79
1016.99 443.26
1009.3 432.04
1013.32 465.86
1009.05 465.6
1009.35 469.43
1003.4 440.75
1015.82 481.32
1022.64 479.87
1005.7 458.59
1009.62 438.62
1012.38 445.59
1015.13 481.87
1013.58 475.01
1008.53 436.54
1016.28 456.63
1015.63 451.69
1010.93 463.04
1007.68 446.1
1009.94 438.67
1019.7 466.88
1008.42 444.6
1015.4 440.26
1023.28 483.92
1017.18 475.19
1023.06 479.24
1014.95 434.92
1014.0 454.16
1012.42 447.58
1021.67 467.9
1010.27 426.29
1007.8 447.02
1005.47 455.85
1010.31 476.46
1007.53 437.48
1014.61 452.77
1012.57 491.54
1017.22 438.41
1019.81 476.1
1007.87 464.58
1023.91 467.74
1010.0 442.12
1014.53 453.34
1010.44 425.29
1011.74 449.63
1025.27 462.88
1015.71 464.67
1027.17 489.96
1020.27 482.38
1009.45 437.95
1004.74 429.2
1013.03 453.34
1010.58 442.47
1015.14 462.6
1024.57 478.79
1012.34 456.11
1005.81 450.33
1007.21 434.83
1015.1 433.43
1020.76 456.02
1018.08 485.23
1013.03 473.57
1011.17 469.94
1008.69 452.07
1021.82 475.32
1013.39 480.69
1013.12 444.01
1020.41 465.17
1012.87 480.61
1013.39 476.04
1003.51 441.76
1005.19 428.24
1004.0 444.77
1008.58 463.1
1018.19 470.5
1007.04 431.0
1004.27 430.68
1006.6 436.42
1016.19 452.33
1010.64 440.16
1010.18 435.75
1008.48 449.74
1010.74 430.73
1009.55 432.75
1007.88 446.79
1018.12 486.35
1015.66 453.18
1015.73 458.31
1019.7 480.26
1011.89 448.65
1012.67 458.41
1006.37 435.39
1010.49 450.21
1018.68 459.59
1017.19 445.84
1018.17 441.08
1009.89 467.33
1016.56 444.19
1007.96 432.96
1002.85 438.09
1006.86 467.9
1012.68 475.72
1027.72 477.51
1006.37 435.13
1017.99 477.9
1019.18 457.26
1015.88 467.53
1021.08 465.15
1014.42 474.28
1013.85 444.49
1014.15 452.84
1008.5 435.38
1003.88 433.57
1009.04 435.27
1005.35 468.49
1009.9 433.07
1004.85 430.63
1013.29 440.74
1026.31 474.49
1005.72 449.74
1010.09 436.73
1006.53 434.58
1017.24 473.93
1007.03 435.99
1009.45 466.83
1005.29 427.22
1013.39 444.07
1020.11 469.57
1015.18 459.89
1024.91 479.59
1007.21 440.92
1020.45 480.87
1009.93 441.9
1011.35 430.2
1014.62 465.16
1021.19 471.32
1020.91 485.43
1012.27 495.35
1010.85 449.12
1006.22 480.53
1014.89 457.07
1010.7 443.67
1023.44 477.52
1012.52 472.95
1003.92 472.54
1015.85 469.17
1011.09 435.21
1004.81 477.78
1012.86 475.89
1017.75 483.9
1016.53 476.2
1015.47 462.16
1011.24 471.05
1010.6 484.71
1015.43 446.34
1007.21 469.02
1004.23 432.12
1015.51 467.28
1013.29 429.66
1013.16 469.49
1023.23 485.87
1026.0 481.95
1031.1 479.03
1010.99 434.5
1015.16 464.9
1020.02 452.71
1010.84 429.74
1020.67 457.09
1011.61 446.77
1014.46 460.76
1008.31 471.95
1014.09 453.29
1016.34 441.61
1017.01 464.73
1016.91 464.68
1003.72 430.59
1014.19 438.01
1021.84 479.08
1009.28 436.39
1016.25 447.07
1011.9 479.91
1013.88 489.05
1016.46 463.17
1001.18 471.26
1011.64 480.49
1025.41 473.78
1016.76 455.5
1013.78 446.27
1021.21 482.2
1016.72 452.48
1011.92 464.48
1015.29 438.1
1012.77 445.6
1010.37 442.43
1011.56 436.67
1016.54 466.56
1019.65 457.29
1029.65 487.03
1026.45 464.93
1019.28 466.0
1017.44 469.52
1011.18 428.88
1018.49 474.3
1009.69 461.06
1014.09 465.57
1012.3 467.67
1016.02 466.99
1013.73 463.72
1004.03 443.78
1005.43 445.23
1017.13 464.43
1028.31 484.36
1012.5 442.16
1004.64 464.11
1018.35 462.48
1009.59 477.49
1012.78 437.04
1003.8 457.09
1012.22 450.6
1023.25 465.78
1010.15 427.1
1020.14 459.81
1006.64 447.36
1011.0 488.92
1012.96 433.36
1021.99 483.35
1026.57 469.53
1012.27 476.96
1017.5 440.75
1024.51 462.55
1012.05 448.04
1016.22 455.24
1011.8 494.75
1012.55 444.58
1011.56 484.82
1019.6 442.9
1009.68 485.46
1012.82 457.81
1013.85 481.92
1009.63 443.23
1000.91 474.29
1009.98 430.46
1013.56 455.71
1011.25 438.34
1003.24 485.83
1017.76 452.82
1007.68 435.04
1016.82 451.21
1028.41 465.81
1025.04 458.42
1026.09 470.22
1020.84 449.24
1023.84 471.43
1023.74 473.26
1011.7 452.82
1008.1 432.69
1017.91 444.13
1029.8 467.21
1002.33 445.98
1002.42 436.91
1009.05 455.01
1002.47 437.11
1020.68 477.06
1006.65 441.71
1019.63 495.76
1011.33 445.63
1012.88 464.72
1005.94 438.03
1003.47 434.78
1015.63 444.67
1012.2 452.24
1014.19 450.92
1006.65 436.53
1005.75 435.53
1013.23 440.01
1008.72 443.1
1007.18 427.49
1012.99 436.25
1009.99 440.74
1015.02 443.54
1010.82 459.42
1009.76 439.66
1023.55 464.15
1020.55 459.1
1014.76 455.68
1015.33 469.08
1007.71 478.02
1017.36 456.8
1009.18 441.13
1017.05 463.88
1006.14 430.45
1014.24 449.18
1010.92 447.89
1010.4 431.59
1009.36 447.5
1033.04 475.58
1016.77 453.24
1012.59 446.4
1025.1 476.81
1019.29 474.1
1016.66 450.71
1006.4 433.62
1011.45 465.14
1019.08 445.18
1015.3 474.12
1016.08 483.91
1010.55 486.68
1022.43 464.98
1010.83 481.4
1021.81 479.2
1005.85 463.86
1012.76 472.3
1001.31 446.51
1005.93 437.71
1001.96 458.94
1007.62 437.91
1009.96 490.76
1013.4 439.66
1007.58 463.27
1016.68 473.99
1012.83 433.38
1015.13 459.01
1016.05 471.44
1012.97 471.91
1028.2 465.15
1008.25 446.66
1009.78 438.15
1008.81 447.14
1025.53 472.32
1010.16 441.68
1009.33 440.04
1009.82 444.82
1014.5 457.26
1009.13 428.83
1009.93 449.07
1009.38 435.21
1017.59 471.03
1012.47 465.56
1019.86 442.83
1017.26 460.3
1023.07 474.25
1033.3 477.97
1019.1 472.16
1014.22 456.08
1014.9 452.41
1011.31 463.71
1006.26 433.72
1016.0 456.4
1015.41 448.43
1020.63 481.6
1001.16 457.07
1019.8 451.0
1018.48 440.28
1002.26 437.47
1004.07 443.57
1004.91 426.6
1013.12 470.87
1012.9 478.37
1013.32 453.92
1020.79 470.22
1011.37 434.54
1013.11 442.89
1013.29 479.03
1020.5 476.06
1022.62 473.88
1010.84 451.75
1012.68 439.2
1015.58 439.7
1013.68 463.6
1004.21 447.47
1013.23 447.92
1020.44 471.08
1007.99 437.55
1012.36 448.27
998.47 431.69
1016.57 449.09
1015.93 448.79
1025.21 460.21
1013.54 479.28
1032.67 483.11
1011.46 450.75
1010.43 437.97
1008.53 459.76
1020.5 457.75
1015.48 469.33
1009.74 433.28
1010.23 444.64
1021.3 463.1
1022.01 460.91
1023.95 479.35
1017.65 449.23
1021.83 474.51
1007.81 435.02
1009.43 435.45
1013.3 452.38
1019.73 480.41
1019.54 478.96
1026.58 468.87
1007.89 434.01
1013.85 466.36
1011.44 435.28
1014.51 486.46
1015.51 468.19
1022.14 468.37
1019.17 474.19
1009.52 440.32
1015.35 485.32
1014.38 464.27
1013.66 479.25
1007.0 430.4
1016.65 447.49
1006.85 438.23
1025.46 492.09
1015.13 475.36
1016.68 452.56
1015.98 427.84
1010.8 433.95
1008.48 435.27
1014.04 454.62
1020.36 472.17
1015.96 452.42
1003.19 472.17
1018.01 481.83
1021.83 458.78
1022.47 447.5
1019.04 463.4
1022.67 473.57
1009.07 433.72
1011.2 431.85
1012.13 433.47
1007.45 432.84
1007.29 436.6
1020.12 490.23
1020.58 477.16
1010.44 441.06
1007.22 440.86
1033.08 477.94
1026.56 474.47
1012.18 470.67
1013.7 447.31
1018.14 466.8
1007.4 430.91
1007.2 434.75
1010.82 469.52
1008.88 438.9
1010.51 429.56
1013.53 432.92
1005.68 442.87
1022.57 466.59
1028.04 479.61
1019.12 471.08
1016.51 433.37
1018.8 443.92
1016.74 443.5
1017.37 439.89
1008.9 434.66
1021.95 487.57
1013.76 464.64
1017.26 470.92
1014.37 444.39
1002.54 442.48
1005.25 449.61
1009.43 435.02
1021.81 458.67
1016.63 461.74
1008.09 438.31
1011.68 462.38
1019.39 460.56
1013.37 439.22
1009.71 444.64
999.8 430.34
1008.37 430.46
1009.02 456.79
994.17 468.82
1008.79 448.51
1014.67 470.77
1025.79 465.74
1005.31 430.21
1008.62 449.23
1021.91 461.89
1010.97 445.72
1013.36 466.13
1008.38 448.71
998.43 469.25
1013.04 450.56
1008.94 464.46
1014.87 471.13
1010.92 461.52
1012.04 451.09
1005.43 431.51
1009.65 469.8
1012.05 442.28
1011.84 458.67
1016.13 462.4
1015.18 453.54
1019.81 444.38
1003.39 440.52
1007.68 433.62
1023.68 481.96
1008.89 452.75
1026.4 481.28
1020.28 439.03
1005.64 435.75
1009.72 436.03
1011.03 445.6
1020.27 462.65
1005.87 438.66
1008.54 447.32
1004.85 484.55
1024.9 476.8
1023.99 480.34
1010.53 440.63
1014.27 459.48
1025.98 490.78
1019.25 483.56
1012.26 429.38
1013.49 440.27
1011.34 445.34
1013.86 447.43
1004.37 439.91
1016.11 459.27
1017.88 478.89
1012.41 466.7
1021.39 463.5
1015.04 436.21
1011.95 443.94
1012.87 439.63
1013.21 460.95
1015.99 448.69
1006.24 444.63
1005.49 473.51
1008.56 462.56
1011.07 451.76
1025.68 491.81
1011.04 429.52
1007.59 437.9
1003.18 467.54
1015.35 449.97
1003.61 436.62
1023.37 477.68
1016.04 447.26
1011.8 439.76
1015.23 437.49
1018.29 455.14
1021.76 485.5
1016.81 444.1
1006.91 432.33
1008.87 471.23
1017.93 463.89
1009.2 445.54
1007.99 446.09
1017.82 445.12
1018.29 443.31
1015.14 484.16
1019.86 477.76
1008.36 430.28
1010.39 446.48
1028.11 481.03
1007.41 466.07
1013.2 447.47
1019.83 455.93
1021.15 479.62
1014.28 455.06
1019.87 475.06
1012.59 438.89
1003.38 432.7
1011.89 452.6
1010.46 451.75
1008.16 430.66
1019.04 491.9
1010.04 439.82
1015.91 460.73
1015.14 449.7
1013.88 439.42
1013.33 439.84
1025.58 485.86
1011.81 458.1
1012.89 479.92
1019.94 458.29
1017.29 489.45
1012.17 434.0
1010.69 431.24
1003.26 439.5
1019.48 467.46
1010.0 429.27
1016.95 452.1
999.83 472.41
1002.75 442.14
1003.56 441.0
1020.76 463.07
1017.99 445.71
1017.11 483.16
1010.75 440.45
1020.6 481.83
1015.53 467.6
1004.29 450.88
1001.22 425.5
1013.95 451.87
1010.51 428.94
1002.59 439.86
1011.21 433.44
1015.12 438.23
1007.68 436.95
1021.67 470.19
1011.6 484.66
1007.56 430.81
1010.05 433.37
1014.17 453.02
1012.6 453.5
995.88 463.09
1016.25 464.56
1017.22 452.12
1015.66 470.9
1021.08 450.89
1009.85 445.04
1011.49 444.72
1022.07 460.38
1013.05 446.8
1018.34 465.05
1016.55 484.13
1017.01 488.27
1013.85 447.09
1017.16 452.02
1014.16 455.55
1029.41 480.99
1012.96 467.68
Humidity Power
73.17 463.26
59.08 444.37
92.14 488.56
76.64 446.48
96.62 473.9
58.77 443.67
75.24 467.35
66.43 478.42
41.25 475.98
70.72 477.5
75.04 453.02
64.22 453.99
84.15 440.29
61.83 451.28
87.59 433.99
43.08 462.19
48.84 467.54
77.51 477.2
63.59 459.85
55.28 464.3
66.26 468.27
64.77 495.24
83.31 483.8
47.19 443.61
54.93 436.06
74.62 443.25
72.52 464.16
88.44 475.52
92.28 484.41
41.85 437.89
44.28 445.11
64.58 438.86
63.25 440.98
78.61 436.65
44.51 444.26
89.46 465.86
74.52 444.37
88.86 450.69
75.51 469.02
78.64 448.86
76.65 447.14
80.44 469.18
79.89 482.8
88.28 476.7
84.6 474.99
42.69 444.22
78.41 461.33
61.07 448.06
50.0 474.6
77.29 473.05
43.66 432.06
83.8 467.41
66.47 430.12
93.09 473.62
80.52 471.81
68.99 442.99
57.27 442.77
95.53 491.49
71.72 447.46
57.88 446.11
63.34 442.44
48.07 446.22
91.87 471.49
87.27 463.5
64.4 440.01
43.4 441.03
72.24 452.68
90.22 474.91
74.0 478.77
71.85 434.2
86.62 437.91
97.41 477.61
84.44 431.65
81.55 430.57
75.66 481.09
79.41 445.56
58.91 475.74
90.06 435.12
79.0 446.15
69.47 436.64
51.47 436.69
83.13 468.75
40.33 466.6
81.69 465.48
94.55 441.34
91.81 441.83
63.62 464.7
49.35 437.99
69.61 459.12
38.75 429.69
90.17 459.8
81.24 433.63
48.46 442.84
76.72 485.13
51.16 459.12
76.34 445.31
67.3 480.8
52.38 432.55
76.44 443.86
91.55 449.77
71.9 470.71
80.05 452.17
63.77 478.29
62.26 428.54
89.04 478.27
58.02 439.58
81.82 457.32
91.14 475.51
88.92 439.66
84.83 471.99
91.76 479.81
86.56 434.78
57.21 446.58
54.25 437.76
63.8 459.36
33.71 462.28
67.25 464.33
60.11 444.36
74.55 438.64
67.34 470.49
42.75 455.13
55.2 450.22
83.61 440.43
88.78 482.98
100.12 460.44
64.52 444.97
51.41 433.94
85.78 439.73
75.41 434.48
81.63 442.33
51.92 457.67
70.12 454.66
53.83 432.21
77.23 457.66
65.67 435.21
71.18 448.22
81.96 475.51
79.54 446.53
47.09 441.3
57.69 433.54
78.89 472.52
85.29 474.77
40.13 435.1
77.06 450.74
67.38 442.7
62.44 426.56
77.43 463.71
58.77 447.06
67.72 452.27
42.14 445.78
84.16 438.65
89.79 480.15
67.21 447.19
72.14 443.04
97.49 488.81
87.74 455.75
96.3 455.86
61.25 457.68
88.38 479.11
74.77 432.84
68.18 448.37
77.2 447.06
49.54 443.53
92.22 445.21
33.65 441.7
64.59 450.93
100.09 451.44
68.04 441.29
48.94 458.85
74.47 481.46
81.02 467.19
71.17 461.54
53.85 439.08
70.67 467.22
59.36 468.8
57.17 426.93
70.29 474.65
83.37 468.97
87.36 433.97
100.09 450.53
68.78 444.51
70.98 469.03
75.68 466.56
47.49 457.57
71.99 440.13
66.55 433.24
74.73 452.55
64.78 443.29
75.13 431.76
56.38 454.97
94.35 456.7
86.55 486.03
82.95 472.79
88.42 452.03
85.61 443.41
58.39 441.93
74.28 432.64
87.85 480.25
83.5 466.68
65.24 494.39
75.01 454.72
84.52 448.71
80.52 469.76
75.14 450.71
75.75 444.01
76.72 453.2
85.47 450.87
57.95 441.73
78.32 465.09
52.2 447.28
93.69 491.16
75.74 450.98
67.56 446.3
69.46 436.48
74.58 460.84
53.23 442.56
88.72 467.3
96.16 479.13
68.26 441.15
86.39 445.52
85.34 475.4
72.64 469.3
97.82 463.57
77.22 445.32
80.59 461.03
46.91 466.74
57.76 444.04
53.09 434.01
84.31 465.23
71.58 440.6
92.97 466.74
74.55 433.48
78.96 473.59
64.44 474.81
68.23 454.75
70.81 452.94
61.66 435.83
77.76 482.19
69.49 466.66
96.26 462.59
55.74 447.82
95.61 462.73
84.75 447.98
75.3 462.72
67.5 442.42
80.92 444.69
79.23 466.7
81.1 453.84
32.8 436.92
84.31 486.37
46.15 440.43
53.96 446.82
59.83 484.91
75.3 437.76
42.53 438.91
70.58 464.19
91.69 442.19
63.55 446.86
61.51 457.15
69.55 482.57
98.08 476.03
79.34 428.89
81.28 472.7
78.99 445.6
80.38 464.78
51.16 440.42
72.17 428.41
75.39 438.5
68.91 438.28
96.38 476.29
70.54 448.46
45.8 438.99
57.95 471.8
81.89 471.81
69.32 449.82
59.14 442.14
81.54 441.46
85.81 477.62
65.41 446.76
81.15 472.52
95.87 471.58
90.24 440.85
75.13 431.37
88.22 437.33
81.48 469.22
89.84 471.11
43.57 439.17
63.16 445.33
57.14 473.71
77.76 452.66
90.56 440.99
60.98 467.42
70.31 444.14
74.05 457.17
75.42 467.87
82.25 442.04
67.95 471.36
100.09 460.7
47.28 431.33
72.41 432.6
77.67 447.61
63.7 443.87
79.77 446.87
93.84 465.74
84.95 447.86
70.16 447.65
84.24 437.87
73.32 483.51
86.17 479.65
65.43 455.16
94.59 431.91
86.8 470.68
58.18 429.28
89.66 450.81
87.39 437.73
36.35 460.21
79.62 442.86
50.52 482.99
51.96 440.0
74.73 478.48
78.33 455.28
85.19 436.94
83.13 461.06
53.49 438.28
88.86 472.61
60.89 426.85
61.14 470.18
68.29 455.38
57.62 428.32
83.63 480.35
78.1 455.56
66.34 447.66
79.02 443.06
68.96 452.43
71.13 477.81
87.01 431.66
74.3 431.8
77.62 446.67
59.56 445.26
41.66 425.72
73.27 430.58
77.16 439.86
67.02 441.11
52.8 434.72
39.04 434.01
65.47 475.64
74.32 460.44
69.22 436.4
93.88 461.03
69.83 479.08
84.11 435.76
78.65 460.14
69.31 442.2
70.3 447.69
68.23 431.15
71.76 445.0
85.88 431.59
71.09 467.22
52.67 445.33
89.68 470.57
73.66 473.77
58.94 447.67
87.05 474.29
67.0 437.14
43.18 432.56
80.62 459.14
59.72 446.19
72.1 428.1
69.15 468.46
55.66 435.02
61.19 445.52
74.62 462.69
73.35 455.75
68.85 463.74
39.89 439.79
53.16 443.26
52.97 432.04
79.87 465.86
84.09 465.6
100.15 469.43
79.77 440.75
88.99 481.32
76.14 479.87
69.13 458.59
93.03 438.62
77.92 445.59
74.89 481.87
88.7 475.01
62.94 436.54
89.62 456.63
81.04 451.69
94.53 463.04
64.02 446.1
70.57 438.67
70.32 466.88
84.86 444.6
81.41 440.26
89.45 483.92
82.71 475.19
93.93 479.24
70.6 434.92
87.68 454.16
87.58 447.58
74.4 467.9
67.35 426.29
63.61 447.02
76.89 455.85
78.08 476.46
69.17 437.48
53.31 452.77
93.32 491.54
42.47 438.41
82.58 476.1
94.59 464.58
86.31 467.74
72.57 442.12
80.76 453.34
71.93 425.29
47.54 449.63
95.72 462.88
77.03 464.67
80.49 489.96
77.67 482.38
78.72 437.95
58.77 429.2
74.8 453.34
51.34 442.47
90.41 462.6
91.1 478.79
62.57 456.11
84.27 450.33
42.93 434.83
40.96 433.43
76.53 456.02
69.74 485.23
74.99 473.57
70.45 469.94
91.49 452.07
88.97 475.32
89.13 480.69
46.52 444.01
60.55 465.17
88.71 480.61
89.15 476.04
83.02 441.76
75.19 428.24
87.35 444.77
85.66 463.1
91.66 470.5
63.47 431.0
72.25 430.68
70.58 436.42
60.1 452.33
89.29 440.16
67.43 435.75
67.58 449.74
70.8 430.73
63.62 432.75
66.68 446.79
90.76 486.35
75.34 453.18
59.77 458.31
80.79 480.26
74.1 448.65
41.34 458.41
58.78 435.39
97.78 450.21
74.85 459.59
69.84 445.84
75.36 441.08
85.8 467.33
90.11 444.19
61.63 432.96
44.76 438.09
89.7 467.9
72.51 475.72
74.98 477.51
79.59 435.13
78.42 477.9
61.23 457.26
47.56 467.53
93.06 465.15
89.65 474.28
50.5 444.49
44.84 452.84
85.32 435.38
82.94 433.57
67.26 435.27
79.05 468.49
62.03 433.07
94.36 430.63
60.02 440.74
95.46 474.49
84.92 449.74
62.8 436.73
90.81 434.58
80.9 473.93
55.84 435.99
75.3 466.83
37.34 427.22
79.5 444.07
87.29 469.57
81.5 459.89
76.42 479.59
75.75 440.92
84.95 480.87
62.37 441.9
49.25 430.2
74.16 465.16
90.55 471.32
94.28 485.43
63.31 495.35
78.9 449.12
90.97 480.53
87.34 457.07
80.8 443.67
90.95 477.52
69.97 472.95
89.45 472.54
76.08 469.17
83.35 435.21
92.16 477.78
58.42 475.89
85.06 483.9
88.91 476.2
83.33 462.16
88.49 471.05
96.88 484.71
73.86 446.34
65.17 469.02
69.41 432.12
81.23 467.28
54.07 429.66
89.17 469.49
78.85 485.87
84.44 481.95
83.02 479.03
90.66 434.5
75.29 464.9
82.6 452.71
45.4 429.74
66.33 457.09
45.33 446.77
67.12 460.76
84.14 471.95
80.81 453.29
49.13 441.61
87.29 464.73
52.95 464.68
68.92 430.59
85.21 438.01
88.56 479.08
55.09 436.39
48.64 447.07
87.85 479.91
87.42 489.05
62.75 463.17
94.86 471.26
63.54 480.49
69.46 473.78
74.66 455.5
80.57 446.27
84.7 482.2
72.6 452.48
52.63 464.48
82.01 438.1
75.22 445.6
51.05 442.43
80.1 436.67
81.58 466.56
65.94 457.29
86.74 487.03
62.57 464.93
57.37 466.0
88.91 469.52
72.26 428.88
74.98 474.3
71.19 461.06
62.82 465.57
55.31 467.67
71.57 466.99
59.16 463.72
40.8 443.78
67.63 445.23
97.2 464.43
91.16 484.36
64.81 442.16
85.61 464.11
93.42 462.48
77.36 477.49
67.03 437.04
89.45 457.09
54.84 450.6
53.48 465.78
54.47 427.1
43.36 459.81
48.92 447.36
81.22 488.92
60.35 433.36
75.98 483.35
74.24 469.53
85.21 476.96
68.46 440.75
78.31 462.55
89.25 448.04
68.57 455.24
67.38 494.75
53.6 444.58
91.69 484.82
78.21 442.9
94.19 485.46
37.19 457.81
83.53 481.92
79.45 443.23
99.9 474.29
50.39 430.46
74.33 455.71
83.66 438.34
89.48 485.83
64.59 452.82
75.68 435.04
64.18 451.21
70.09 465.81
70.58 458.42
99.28 470.22
81.89 449.24
87.99 471.43
88.21 473.26
91.29 452.82
52.72 432.69
67.5 444.13
92.05 467.21
63.23 445.98
90.88 436.91
74.91 455.01
85.39 437.11
96.98 477.06
56.28 441.71
65.62 495.76
55.32 445.63
88.88 464.72
39.49 438.03
54.59 434.78
57.19 444.67
45.06 452.24
40.62 450.92
90.21 436.53
90.91 435.53
74.96 440.01
54.21 443.1
63.62 427.49
50.04 436.25
51.23 440.74
82.71 443.54
92.04 459.42
90.67 439.66
91.14 464.15
70.43 459.1
66.63 455.68
86.95 469.08
96.69 478.02
70.88 456.8
47.14 441.13
63.36 463.88
60.58 430.45
54.3 449.18
65.09 447.89
48.16 431.59
81.51 447.5
68.57 475.58
73.16 453.24
80.88 446.4
85.4 476.81
75.77 474.1
75.76 450.71
70.21 433.62
55.53 465.14
80.48 445.18
72.41 474.12
83.25 483.91
82.12 486.68
94.75 464.98
95.79 481.4
86.02 479.2
78.29 463.86
82.23 472.3
52.86 446.51
60.66 437.71
62.77 458.94
65.54 437.91
95.4 490.76
51.78 439.66
63.62 463.27
83.09 473.99
61.81 433.38
68.24 459.01
72.41 471.44
79.64 471.91
66.95 465.15
91.98 446.66
64.96 438.15
88.93 447.14
85.62 472.32
84.0 441.68
89.41 440.04
67.4 444.82
76.75 457.26
89.06 428.83
64.02 449.07
64.12 435.21
81.22 471.03
100.13 465.56
58.07 442.83
63.42 460.3
83.32 474.25
74.28 477.97
71.91 472.16
85.8 456.08
55.58 452.41
69.7 463.71
63.79 433.72
86.59 456.4
48.28 448.43
80.42 481.6
98.58 457.07
72.83 451.0
56.07 440.28
67.13 437.47
84.49 443.57
68.37 426.6
86.07 470.87
83.82 478.37
74.86 453.92
53.52 470.22
80.61 434.54
43.56 442.89
89.35 479.03
97.28 476.06
80.49 473.88
88.9 451.75
49.7 439.2
68.64 439.7
98.58 463.6
82.12 447.47
78.32 447.92
86.04 471.08
91.36 437.55
81.02 448.27
76.05 431.69
71.81 449.09
82.13 448.79
74.27 460.21
71.32 479.28
74.59 483.11
84.44 450.75
43.39 437.97
87.2 459.76
77.11 457.75
82.81 469.33
85.67 433.28
95.58 444.64
74.46 463.1
90.02 460.91
81.93 479.35
86.29 449.23
85.43 474.51
71.66 435.02
71.33 435.45
67.72 452.38
84.23 480.41
74.44 478.96
71.48 468.87
56.3 434.01
68.13 466.36
68.35 435.28
85.23 486.46
79.78 468.19
98.98 468.37
72.87 474.19
90.93 440.32
72.94 485.32
72.3 464.27
77.74 479.25
78.29 430.4
69.1 447.49
55.79 438.23
75.09 492.09
88.98 475.36
64.26 452.56
25.89 427.84
59.18 433.95
67.48 435.27
89.85 454.62
50.62 472.17
83.97 452.42
96.51 472.17
80.09 481.83
84.02 458.78
61.97 447.5
88.51 463.4
81.83 473.57
90.63 433.72
73.37 431.85
77.5 433.47
57.46 432.84
51.91 436.6
79.14 490.23
69.24 477.16
41.85 441.06
95.1 440.86
74.53 477.94
64.85 474.47
57.07 470.67
62.9 447.31
72.21 466.8
65.99 430.91
73.67 434.75
88.59 469.52
61.19 438.9
49.37 429.56
48.65 432.92
56.18 442.87
71.56 466.59
87.46 479.61
70.02 471.08
61.2 433.37
60.54 443.92
71.82 443.5
44.8 439.89
67.32 434.66
78.77 487.57
96.02 464.64
90.56 470.92
83.19 444.39
68.45 442.48
99.19 449.61
88.11 435.02
79.29 458.67
87.76 461.74
82.56 438.31
79.24 462.38
67.24 460.56
58.98 439.22
84.22 444.64
89.12 430.34
50.07 430.46
98.86 456.79
95.79 468.82
70.06 448.51
41.71 470.77
86.55 465.74
71.97 430.21
96.4 449.23
91.73 461.89
91.62 445.72
59.14 466.13
92.56 448.71
83.71 469.25
55.43 450.56
74.91 464.46
89.41 471.13
69.81 461.52
86.01 451.09
86.05 431.51
80.98 469.8
63.62 442.28
64.16 458.67
75.63 462.4
80.21 453.54
59.7 444.38
47.6 440.52
63.78 433.62
89.37 481.96
70.55 452.75
84.42 481.28
80.62 439.03
52.56 435.75
83.26 436.03
70.64 445.6
89.95 462.65
51.53 438.66
84.83 447.32
59.68 484.55
97.88 476.8
85.03 480.34
47.38 440.63
48.08 459.48
79.65 490.78
83.39 483.56
82.18 429.38
51.71 440.27
77.33 445.34
72.81 447.43
84.26 439.91
73.23 459.27
79.73 478.89
62.32 466.7
78.58 463.5
79.88 436.21
65.87 443.94
80.28 439.63
71.33 460.95
70.33 448.69
57.73 444.63
99.46 473.51
68.61 462.56
95.91 451.76
80.42 491.81
51.01 429.52
74.08 437.9
80.73 467.54
54.71 449.97
73.75 436.62
88.43 477.68
74.66 447.26
70.04 439.76
74.64 437.49
85.11 455.14
82.97 485.5
55.59 444.1
49.9 432.33
89.99 471.23
91.61 463.89
82.95 445.54
92.62 446.09
59.64 445.12
63.0 443.31
85.38 484.16
85.23 477.76
52.08 430.28
38.05 446.48
71.98 481.03
90.66 466.07
83.14 447.47
65.22 455.93
91.67 479.62
66.04 455.06
78.19 475.06
54.47 438.89
67.26 432.7
72.56 452.6
82.15 451.75
86.32 430.66
88.17 491.9
72.78 439.82
69.58 460.73
69.86 449.7
65.37 439.42
52.37 439.84
79.63 485.86
83.14 458.1
88.25 479.92
55.85 458.29
52.55 489.45
62.74 434.0
90.08 431.24
54.5 439.5
49.88 467.46
48.96 429.27
86.77 452.1
96.66 472.41
70.84 442.14
83.83 441.0
68.22 463.07
82.22 445.71
87.9 483.16
66.83 440.45
85.36 481.83
60.9 467.6
83.51 450.88
52.96 425.5
73.02 451.87
43.11 428.94
61.41 439.86
65.32 433.44
93.68 438.23
42.39 436.95
68.18 470.19
89.18 484.66
64.79 430.81
43.48 433.37
80.4 453.02
72.43 453.5
80.0 463.09
45.65 464.56
63.02 452.12
74.39 470.9
57.77 450.89
76.8 445.04
67.39 444.72
73.96 460.38
72.75 446.8
71.69 465.05
84.98 484.13
87.68 488.27
50.36 447.09
68.11 452.02
66.27 455.55
89.72 480.99
61.07 467.68
RH PE
73.17 463.26
59.08 444.37
92.14 488.56
76.64 446.48
96.62 473.9
58.77 443.67
75.24 467.35
66.43 478.42
41.25 475.98
70.72 477.5
75.04 453.02
64.22 453.99
84.15 440.29
61.83 451.28
87.59 433.99
43.08 462.19
48.84 467.54
77.51 477.2
63.59 459.85
55.28 464.3
66.26 468.27
64.77 495.24
83.31 483.8
47.19 443.61
54.93 436.06
74.62 443.25
72.52 464.16
88.44 475.52
92.28 484.41
41.85 437.89
44.28 445.11
64.58 438.86
63.25 440.98
78.61 436.65
44.51 444.26
89.46 465.86
74.52 444.37
88.86 450.69
75.51 469.02
78.64 448.86
76.65 447.14
80.44 469.18
79.89 482.8
88.28 476.7
84.6 474.99
42.69 444.22
78.41 461.33
61.07 448.06
50.0 474.6
77.29 473.05
43.66 432.06
83.8 467.41
66.47 430.12
93.09 473.62
80.52 471.81
68.99 442.99
57.27 442.77
95.53 491.49
71.72 447.46
57.88 446.11
63.34 442.44
48.07 446.22
91.87 471.49
87.27 463.5
64.4 440.01
43.4 441.03
72.24 452.68
90.22 474.91
74.0 478.77
71.85 434.2
86.62 437.91
97.41 477.61
84.44 431.65
81.55 430.57
75.66 481.09
79.41 445.56
58.91 475.74
90.06 435.12
79.0 446.15
69.47 436.64
51.47 436.69
83.13 468.75
40.33 466.6
81.69 465.48
94.55 441.34
91.81 441.83
63.62 464.7
49.35 437.99
69.61 459.12
38.75 429.69
90.17 459.8
81.24 433.63
48.46 442.84
76.72 485.13
51.16 459.12
76.34 445.31
67.3 480.8
52.38 432.55
76.44 443.86
91.55 449.77
71.9 470.71
80.05 452.17
63.77 478.29
62.26 428.54
89.04 478.27
58.02 439.58
81.82 457.32
91.14 475.51
88.92 439.66
84.83 471.99
91.76 479.81
86.56 434.78
57.21 446.58
54.25 437.76
63.8 459.36
33.71 462.28
67.25 464.33
60.11 444.36
74.55 438.64
67.34 470.49
42.75 455.13
55.2 450.22
83.61 440.43
88.78 482.98
100.12 460.44
64.52 444.97
51.41 433.94
85.78 439.73
75.41 434.48
81.63 442.33
51.92 457.67
70.12 454.66
53.83 432.21
77.23 457.66
65.67 435.21
71.18 448.22
81.96 475.51
79.54 446.53
47.09 441.3
57.69 433.54
78.89 472.52
85.29 474.77
40.13 435.1
77.06 450.74
67.38 442.7
62.44 426.56
77.43 463.71
58.77 447.06
67.72 452.27
42.14 445.78
84.16 438.65
89.79 480.15
67.21 447.19
72.14 443.04
97.49 488.81
87.74 455.75
96.3 455.86
61.25 457.68
88.38 479.11
74.77 432.84
68.18 448.37
77.2 447.06
49.54 443.53
92.22 445.21
33.65 441.7
64.59 450.93
100.09 451.44
68.04 441.29
48.94 458.85
74.47 481.46
81.02 467.19
71.17 461.54
53.85 439.08
70.67 467.22
59.36 468.8
57.17 426.93
70.29 474.65
83.37 468.97
87.36 433.97
100.09 450.53
68.78 444.51
70.98 469.03
75.68 466.56
47.49 457.57
71.99 440.13
66.55 433.24
74.73 452.55
64.78 443.29
75.13 431.76
56.38 454.97
94.35 456.7
86.55 486.03
82.95 472.79
88.42 452.03
85.61 443.41
58.39 441.93
74.28 432.64
87.85 480.25
83.5 466.68
65.24 494.39
75.01 454.72
84.52 448.71
80.52 469.76
75.14 450.71
75.75 444.01
76.72 453.2
85.47 450.87
57.95 441.73
78.32 465.09
52.2 447.28
93.69 491.16
75.74 450.98
67.56 446.3
69.46 436.48
74.58 460.84
53.23 442.56
88.72 467.3
96.16 479.13
68.26 441.15
86.39 445.52
85.34 475.4
72.64 469.3
97.82 463.57
77.22 445.32
80.59 461.03
46.91 466.74
57.76 444.04
53.09 434.01
84.31 465.23
71.58 440.6
92.97 466.74
74.55 433.48
78.96 473.59
64.44 474.81
68.23 454.75
70.81 452.94
61.66 435.83
77.76 482.19
69.49 466.66
96.26 462.59
55.74 447.82
95.61 462.73
84.75 447.98
75.3 462.72
67.5 442.42
80.92 444.69
79.23 466.7
81.1 453.84
32.8 436.92
84.31 486.37
46.15 440.43
53.96 446.82
59.83 484.91
75.3 437.76
42.53 438.91
70.58 464.19
91.69 442.19
63.55 446.86
61.51 457.15
69.55 482.57
98.08 476.03
79.34 428.89
81.28 472.7
78.99 445.6
80.38 464.78
51.16 440.42
72.17 428.41
75.39 438.5
68.91 438.28
96.38 476.29
70.54 448.46
45.8 438.99
57.95 471.8
81.89 471.81
69.32 449.82
59.14 442.14
81.54 441.46
85.81 477.62
65.41 446.76
81.15 472.52
95.87 471.58
90.24 440.85
75.13 431.37
88.22 437.33
81.48 469.22
89.84 471.11
43.57 439.17
63.16 445.33
57.14 473.71
77.76 452.66
90.56 440.99
60.98 467.42
70.31 444.14
74.05 457.17
75.42 467.87
82.25 442.04
67.95 471.36
100.09 460.7
47.28 431.33
72.41 432.6
77.67 447.61
63.7 443.87
79.77 446.87
93.84 465.74
84.95 447.86
70.16 447.65
84.24 437.87
73.32 483.51
86.17 479.65
65.43 455.16
94.59 431.91
86.8 470.68
58.18 429.28
89.66 450.81
87.39 437.73
36.35 460.21
79.62 442.86
50.52 482.99
51.96 440.0
74.73 478.48
78.33 455.28
85.19 436.94
83.13 461.06
53.49 438.28
88.86 472.61
60.89 426.85
61.14 470.18
68.29 455.38
57.62 428.32
83.63 480.35
78.1 455.56
66.34 447.66
79.02 443.06
68.96 452.43
71.13 477.81
87.01 431.66
74.3 431.8
77.62 446.67
59.56 445.26
41.66 425.72
73.27 430.58
77.16 439.86
67.02 441.11
52.8 434.72
39.04 434.01
65.47 475.64
74.32 460.44
69.22 436.4
93.88 461.03
69.83 479.08
84.11 435.76
78.65 460.14
69.31 442.2
70.3 447.69
68.23 431.15
71.76 445.0
85.88 431.59
71.09 467.22
52.67 445.33
89.68 470.57
73.66 473.77
58.94 447.67
87.05 474.29
67.0 437.14
43.18 432.56
80.62 459.14
59.72 446.19
72.1 428.1
69.15 468.46
55.66 435.02
61.19 445.52
74.62 462.69
73.35 455.75
68.85 463.74
39.89 439.79
53.16 443.26
52.97 432.04
79.87 465.86
84.09 465.6
100.15 469.43
79.77 440.75
88.99 481.32
76.14 479.87
69.13 458.59
93.03 438.62
77.92 445.59
74.89 481.87
88.7 475.01
62.94 436.54
89.62 456.63
81.04 451.69
94.53 463.04
64.02 446.1
70.57 438.67
70.32 466.88
84.86 444.6
81.41 440.26
89.45 483.92
82.71 475.19
93.93 479.24
70.6 434.92
87.68 454.16
87.58 447.58
74.4 467.9
67.35 426.29
63.61 447.02
76.89 455.85
78.08 476.46
69.17 437.48
53.31 452.77
93.32 491.54
42.47 438.41
82.58 476.1
94.59 464.58
86.31 467.74
72.57 442.12
80.76 453.34
71.93 425.29
47.54 449.63
95.72 462.88
77.03 464.67
80.49 489.96
77.67 482.38
78.72 437.95
58.77 429.2
74.8 453.34
51.34 442.47
90.41 462.6
91.1 478.79
62.57 456.11
84.27 450.33
42.93 434.83
40.96 433.43
76.53 456.02
69.74 485.23
74.99 473.57
70.45 469.94
91.49 452.07
88.97 475.32
89.13 480.69
46.52 444.01
60.55 465.17
88.71 480.61
89.15 476.04
83.02 441.76
75.19 428.24
87.35 444.77
85.66 463.1
91.66 470.5
63.47 431.0
72.25 430.68
70.58 436.42
60.1 452.33
89.29 440.16
67.43 435.75
67.58 449.74
70.8 430.73
63.62 432.75
66.68 446.79
90.76 486.35
75.34 453.18
59.77 458.31
80.79 480.26
74.1 448.65
41.34 458.41
58.78 435.39
97.78 450.21
74.85 459.59
69.84 445.84
75.36 441.08
85.8 467.33
90.11 444.19
61.63 432.96
44.76 438.09
89.7 467.9
72.51 475.72
74.98 477.51
79.59 435.13
78.42 477.9
61.23 457.26
47.56 467.53
93.06 465.15
89.65 474.28
50.5 444.49
44.84 452.84
85.32 435.38
82.94 433.57
67.26 435.27
79.05 468.49
62.03 433.07
94.36 430.63
60.02 440.74
95.46 474.49
84.92 449.74
62.8 436.73
90.81 434.58
80.9 473.93
55.84 435.99
75.3 466.83
37.34 427.22
79.5 444.07
87.29 469.57
81.5 459.89
76.42 479.59
75.75 440.92
84.95 480.87
62.37 441.9
49.25 430.2
74.16 465.16
90.55 471.32
94.28 485.43
63.31 495.35
78.9 449.12
90.97 480.53
87.34 457.07
80.8 443.67
90.95 477.52
69.97 472.95
89.45 472.54
76.08 469.17
83.35 435.21
92.16 477.78
58.42 475.89
85.06 483.9
88.91 476.2
83.33 462.16
88.49 471.05
96.88 484.71
73.86 446.34
65.17 469.02
69.41 432.12
81.23 467.28
54.07 429.66
89.17 469.49
78.85 485.87
84.44 481.95
83.02 479.03
90.66 434.5
75.29 464.9
82.6 452.71
45.4 429.74
66.33 457.09
45.33 446.77
67.12 460.76
84.14 471.95
80.81 453.29
49.13 441.61
87.29 464.73
52.95 464.68
68.92 430.59
85.21 438.01
88.56 479.08
55.09 436.39
48.64 447.07
87.85 479.91
87.42 489.05
62.75 463.17
94.86 471.26
63.54 480.49
69.46 473.78
74.66 455.5
80.57 446.27
84.7 482.2
72.6 452.48
52.63 464.48
82.01 438.1
75.22 445.6
51.05 442.43
80.1 436.67
81.58 466.56
65.94 457.29
86.74 487.03
62.57 464.93
57.37 466.0
88.91 469.52
72.26 428.88
74.98 474.3
71.19 461.06
62.82 465.57
55.31 467.67
71.57 466.99
59.16 463.72
40.8 443.78
67.63 445.23
97.2 464.43
91.16 484.36
64.81 442.16
85.61 464.11
93.42 462.48
77.36 477.49
67.03 437.04
89.45 457.09
54.84 450.6
53.48 465.78
54.47 427.1
43.36 459.81
48.92 447.36
81.22 488.92
60.35 433.36
75.98 483.35
74.24 469.53
85.21 476.96
68.46 440.75
78.31 462.55
89.25 448.04
68.57 455.24
67.38 494.75
53.6 444.58
91.69 484.82
78.21 442.9
94.19 485.46
37.19 457.81
83.53 481.92
79.45 443.23
99.9 474.29
50.39 430.46
74.33 455.71
83.66 438.34
89.48 485.83
64.59 452.82
75.68 435.04
64.18 451.21
70.09 465.81
70.58 458.42
99.28 470.22
81.89 449.24
87.99 471.43
88.21 473.26
91.29 452.82
52.72 432.69
67.5 444.13
92.05 467.21
63.23 445.98
90.88 436.91
74.91 455.01
85.39 437.11
96.98 477.06
56.28 441.71
65.62 495.76
55.32 445.63
88.88 464.72
39.49 438.03
54.59 434.78
57.19 444.67
45.06 452.24
40.62 450.92
90.21 436.53
90.91 435.53
74.96 440.01
54.21 443.1
63.62 427.49
50.04 436.25
51.23 440.74
82.71 443.54
92.04 459.42
90.67 439.66
91.14 464.15
70.43 459.1
66.63 455.68
86.95 469.08
96.69 478.02
70.88 456.8
47.14 441.13
63.36 463.88
60.58 430.45
54.3 449.18
65.09 447.89
48.16 431.59
81.51 447.5
68.57 475.58
73.16 453.24
80.88 446.4
85.4 476.81
75.77 474.1
75.76 450.71
70.21 433.62
55.53 465.14
80.48 445.18
72.41 474.12
83.25 483.91
82.12 486.68
94.75 464.98
95.79 481.4
86.02 479.2
78.29 463.86
82.23 472.3
52.86 446.51
60.66 437.71
62.77 458.94
65.54 437.91
95.4 490.76
51.78 439.66
63.62 463.27
83.09 473.99
61.81 433.38
68.24 459.01
72.41 471.44
79.64 471.91
66.95 465.15
91.98 446.66
64.96 438.15
88.93 447.14
85.62 472.32
84.0 441.68
89.41 440.04
67.4 444.82
76.75 457.26
89.06 428.83
64.02 449.07
64.12 435.21
81.22 471.03
100.13 465.56
58.07 442.83
63.42 460.3
83.32 474.25
74.28 477.97
71.91 472.16
85.8 456.08
55.58 452.41
69.7 463.71
63.79 433.72
86.59 456.4
48.28 448.43
80.42 481.6
98.58 457.07
72.83 451.0
56.07 440.28
67.13 437.47
84.49 443.57
68.37 426.6
86.07 470.87
83.82 478.37
74.86 453.92
53.52 470.22
80.61 434.54
43.56 442.89
89.35 479.03
97.28 476.06
80.49 473.88
88.9 451.75
49.7 439.2
68.64 439.7
98.58 463.6
82.12 447.47
78.32 447.92
86.04 471.08
91.36 437.55
81.02 448.27
76.05 431.69
71.81 449.09
82.13 448.79
74.27 460.21
71.32 479.28
74.59 483.11
84.44 450.75
43.39 437.97
87.2 459.76
77.11 457.75
82.81 469.33
85.67 433.28
95.58 444.64
74.46 463.1
90.02 460.91
81.93 479.35
86.29 449.23
85.43 474.51
71.66 435.02
71.33 435.45
67.72 452.38
84.23 480.41
74.44 478.96
71.48 468.87
56.3 434.01
68.13 466.36
68.35 435.28
85.23 486.46
79.78 468.19
98.98 468.37
72.87 474.19
90.93 440.32
72.94 485.32
72.3 464.27
77.74 479.25
78.29 430.4
69.1 447.49
55.79 438.23
75.09 492.09
88.98 475.36
64.26 452.56
25.89 427.84
59.18 433.95
67.48 435.27
89.85 454.62
50.62 472.17
83.97 452.42
96.51 472.17
80.09 481.83
84.02 458.78
61.97 447.5
88.51 463.4
81.83 473.57
90.63 433.72
73.37 431.85
77.5 433.47
57.46 432.84
51.91 436.6
79.14 490.23
69.24 477.16
41.85 441.06
95.1 440.86
74.53 477.94
64.85 474.47
57.07 470.67
62.9 447.31
72.21 466.8
65.99 430.91
73.67 434.75
88.59 469.52
61.19 438.9
49.37 429.56
48.65 432.92
56.18 442.87
71.56 466.59
87.46 479.61
70.02 471.08
61.2 433.37
60.54 443.92
71.82 443.5
44.8 439.89
67.32 434.66
78.77 487.57
96.02 464.64
90.56 470.92
83.19 444.39
68.45 442.48
99.19 449.61
88.11 435.02
79.29 458.67
87.76 461.74
82.56 438.31
79.24 462.38
67.24 460.56
58.98 439.22
84.22 444.64
89.12 430.34
50.07 430.46
98.86 456.79
95.79 468.82
70.06 448.51
41.71 470.77
86.55 465.74
71.97 430.21
96.4 449.23
91.73 461.89
91.62 445.72
59.14 466.13
92.56 448.71
83.71 469.25
55.43 450.56
74.91 464.46
89.41 471.13
69.81 461.52
86.01 451.09
86.05 431.51
80.98 469.8
63.62 442.28
64.16 458.67
75.63 462.4
80.21 453.54
59.7 444.38
47.6 440.52
63.78 433.62
89.37 481.96
70.55 452.75
84.42 481.28
80.62 439.03
52.56 435.75
83.26 436.03
70.64 445.6
89.95 462.65
51.53 438.66
84.83 447.32
59.68 484.55
97.88 476.8
85.03 480.34
47.38 440.63
48.08 459.48
79.65 490.78
83.39 483.56
82.18 429.38
51.71 440.27
77.33 445.34
72.81 447.43
84.26 439.91
73.23 459.27
79.73 478.89
62.32 466.7
78.58 463.5
79.88 436.21
65.87 443.94
80.28 439.63
71.33 460.95
70.33 448.69
57.73 444.63
99.46 473.51
68.61 462.56
95.91 451.76
80.42 491.81
51.01 429.52
74.08 437.9
80.73 467.54
54.71 449.97
73.75 436.62
88.43 477.68
74.66 447.26
70.04 439.76
74.64 437.49
85.11 455.14
82.97 485.5
55.59 444.1
49.9 432.33
89.99 471.23
91.61 463.89
82.95 445.54
92.62 446.09
59.64 445.12
63.0 443.31
85.38 484.16
85.23 477.76
52.08 430.28
38.05 446.48
71.98 481.03
90.66 466.07
83.14 447.47
65.22 455.93
91.67 479.62
66.04 455.06
78.19 475.06
54.47 438.89
67.26 432.7
72.56 452.6
82.15 451.75
86.32 430.66
88.17 491.9
72.78 439.82
69.58 460.73
69.86 449.7
65.37 439.42
52.37 439.84
79.63 485.86
83.14 458.1
88.25 479.92
55.85 458.29
52.55 489.45
62.74 434.0
90.08 431.24
54.5 439.5
49.88 467.46
48.96 429.27
86.77 452.1
96.66 472.41
70.84 442.14
83.83 441.0
68.22 463.07
82.22 445.71
87.9 483.16
66.83 440.45
85.36 481.83
60.9 467.6
83.51 450.88
52.96 425.5
73.02 451.87
43.11 428.94
61.41 439.86
65.32 433.44
93.68 438.23
42.39 436.95
68.18 470.19
89.18 484.66
64.79 430.81
43.48 433.37
80.4 453.02
72.43 453.5
80.0 463.09
45.65 464.56
63.02 452.12
74.39 470.9
57.77 450.89
76.8 445.04
67.39 444.72
73.96 460.38
72.75 446.8
71.69 465.05
84.98 484.13
87.68 488.27
50.36 447.09
68.11 452.02
66.27 455.55
89.72 480.99
61.07 467.68
AT V AP RH PE
14.96 41.76 1024.07 73.17 463.26
25.18 62.96 1020.04 59.08 444.37
5.11 39.4 1012.16 92.14 488.56
20.86 57.32 1010.24 76.64 446.48
10.82 37.5 1009.23 96.62 473.9
26.27 59.44 1012.23 58.77 443.67
15.89 43.96 1014.02 75.24 467.35
9.48 44.71 1019.12 66.43 478.42
14.64 45.0 1021.78 41.25 475.98
11.74 43.56 1015.14 70.72 477.5
17.99 43.72 1008.64 75.04 453.02
20.14 46.93 1014.66 64.22 453.99
24.34 73.5 1011.31 84.15 440.29
25.71 58.59 1012.77 61.83 451.28
26.19 69.34 1009.48 87.59 433.99
21.42 43.79 1015.76 43.08 462.19
18.21 45.0 1022.86 48.84 467.54
11.04 41.74 1022.6 77.51 477.2
14.45 52.75 1023.97 63.59 459.85
13.97 38.47 1015.15 55.28 464.3
17.76 42.42 1009.09 66.26 468.27
5.41 40.07 1019.16 64.77 495.24
7.76 42.28 1008.52 83.31 483.8
27.23 63.9 1014.3 47.19 443.61
27.36 48.6 1003.18 54.93 436.06
27.47 70.72 1009.97 74.62 443.25
14.6 39.31 1011.11 72.52 464.16
7.91 39.96 1023.57 88.44 475.52
5.81 35.79 1012.14 92.28 484.41
30.53 65.18 1012.69 41.85 437.89
23.87 63.94 1019.02 44.28 445.11
26.09 58.41 1013.64 64.58 438.86
29.27 66.85 1011.11 63.25 440.98
27.38 74.16 1010.08 78.61 436.65
24.81 63.94 1018.76 44.51 444.26
12.75 44.03 1007.29 89.46 465.86
24.66 63.73 1011.4 74.52 444.37
16.38 47.45 1010.08 88.86 450.69
13.91 39.35 1014.69 75.51 469.02
23.18 51.3 1012.04 78.64 448.86
22.47 47.45 1007.62 76.65 447.14
13.39 44.85 1017.24 80.44 469.18
9.28 41.54 1018.33 79.89 482.8
11.82 42.86 1014.12 88.28 476.7
10.27 40.64 1020.63 84.6 474.99
22.92 63.94 1019.28 42.69 444.22
16.0 37.87 1020.24 78.41 461.33
21.22 43.43 1010.96 61.07 448.06
13.46 44.71 1014.51 50.0 474.6
9.39 40.11 1029.14 77.29 473.05
31.07 73.5 1010.58 43.66 432.06
12.82 38.62 1018.71 83.8 467.41
32.57 78.92 1011.6 66.47 430.12
8.11 42.18 1014.82 93.09 473.62
13.92 39.39 1012.94 80.52 471.81
23.04 59.43 1010.23 68.99 442.99
27.31 64.44 1014.65 57.27 442.77
5.91 39.33 1010.18 95.53 491.49
25.26 61.08 1013.68 71.72 447.46
27.97 58.84 1002.25 57.88 446.11
26.08 52.3 1007.03 63.34 442.44
29.01 65.71 1013.61 48.07 446.22
12.18 40.1 1016.67 91.87 471.49
13.76 45.87 1008.89 87.27 463.5
25.5 58.79 1016.02 64.4 440.01
28.26 65.34 1014.56 43.4 441.03
21.39 62.96 1019.49 72.24 452.68
7.26 40.69 1020.43 90.22 474.91
10.54 34.03 1018.71 74.0 478.77
27.71 74.34 998.14 71.85 434.2
23.11 68.3 1017.83 86.62 437.91
7.51 41.01 1024.61 97.41 477.61
26.46 74.67 1016.65 84.44 431.65
29.34 74.34 998.58 81.55 430.57
10.32 42.28 1008.82 75.66 481.09
22.74 61.02 1009.56 79.41 445.56
13.48 39.85 1012.71 58.91 475.74
25.52 69.75 1010.36 90.06 435.12
21.58 67.25 1017.39 79.0 446.15
27.66 76.86 1001.31 69.47 436.64
26.96 69.45 1013.89 51.47 436.69
12.29 42.18 1016.53 83.13 468.75
15.86 43.02 1012.18 40.33 466.6
13.87 45.08 1024.42 81.69 465.48
24.09 73.68 1014.93 94.55 441.34
20.45 69.45 1012.53 91.81 441.83
15.07 39.3 1019.0 63.62 464.7
32.72 69.75 1009.6 49.35 437.99
18.23 58.96 1015.55 69.61 459.12
35.56 68.94 1006.56 38.75 429.69
18.36 51.43 1010.57 90.17 459.8
26.35 64.05 1009.81 81.24 433.63
25.92 60.95 1014.62 48.46 442.84
8.01 41.66 1014.49 76.72 485.13
19.63 52.72 1025.09 51.16 459.12
20.02 67.32 1012.05 76.34 445.31
10.08 40.72 1022.7 67.3 480.8
27.23 66.48 1005.23 52.38 432.55
23.37 63.77 1013.42 76.44 443.86
18.74 59.21 1018.3 91.55 449.77
14.81 43.69 1017.19 71.9 470.71
23.1 51.3 1011.93 80.05 452.17
10.72 41.38 1021.6 63.77 478.29
29.46 71.94 1006.96 62.26 428.54
8.1 40.64 1020.66 89.04 478.27
27.29 62.66 1007.63 58.02 439.58
17.1 49.69 1005.53 81.82 457.32
11.49 44.2 1018.79 91.14 475.51
23.69 65.59 1010.85 88.92 439.66
13.51 40.89 1011.03 84.83 471.99
9.64 39.35 1015.1 91.76 479.81
25.65 78.92 1010.83 86.56 434.78
21.59 61.87 1011.18 57.21 446.58
27.98 58.33 1013.92 54.25 437.76
18.8 39.72 1001.24 63.8 459.36
18.28 44.71 1016.99 33.71 462.28
13.55 43.48 1016.08 67.25 464.33
22.99 46.21 1010.71 60.11 444.36
23.94 59.39 1014.32 74.55 438.64
13.74 34.03 1018.69 67.34 470.49
21.3 41.1 1001.86 42.75 455.13
27.54 66.93 1017.06 55.2 450.22
24.81 63.73 1009.34 83.61 440.43
4.97 42.85 1014.02 88.78 482.98
15.22 50.88 1014.19 100.12 460.44
23.88 54.2 1012.81 64.52 444.97
33.01 68.67 1005.2 51.41 433.94
25.98 73.18 1012.28 85.78 439.73
28.18 73.88 1005.89 75.41 434.48
21.67 60.84 1017.93 81.63 442.33
17.67 45.09 1014.26 51.92 457.67
21.37 57.76 1018.8 70.12 454.66
28.69 67.25 1017.71 53.83 432.21
16.61 43.77 1012.25 77.23 457.66
27.91 63.76 1010.27 65.67 435.21
20.97 47.43 1007.64 71.18 448.22
10.8 41.66 1013.79 81.96 475.51
20.61 62.91 1013.24 79.54 446.53
25.45 57.32 1011.7 47.09 441.3
30.16 69.34 1007.67 57.69 433.54
4.99 39.04 1020.45 78.89 472.52
10.51 44.78 1012.59 85.29 474.77
33.79 69.05 1001.62 40.13 435.1
21.34 59.8 1016.92 77.06 450.74
23.4 65.06 1014.32 67.38 442.7
32.21 68.14 1003.34 62.44 426.56
14.26 42.32 1016.0 77.43 463.71
27.71 66.93 1016.85 58.77 447.06
21.95 57.76 1018.02 67.72 452.27
25.76 63.94 1018.49 42.14 445.78
23.68 68.3 1017.93 84.16 438.65
8.28 40.77 1011.55 89.79 480.15
23.44 62.52 1016.46 67.21 447.19
25.32 48.41 1008.47 72.14 443.04
3.94 39.9 1008.06 97.49 488.81
17.3 57.76 1016.26 87.74 455.75
18.2 49.39 1018.83 96.3 455.86
21.43 46.97 1013.94 61.25 457.68
11.16 40.05 1014.95 88.38 479.11
30.38 74.16 1007.44 74.77 432.84
23.36 62.52 1016.18 68.18 448.37
21.69 47.45 1007.56 77.2 447.06
23.62 49.21 1014.1 49.54 443.53
21.87 61.45 1011.13 92.22 445.21
29.25 66.51 1015.53 33.65 441.7
20.03 66.86 1013.05 64.59 450.93
18.14 49.78 1002.95 100.09 451.44
24.23 56.89 1012.32 68.04 441.29
18.11 44.85 1014.48 48.94 458.85
6.57 43.65 1018.24 74.47 481.46
12.56 43.41 1016.93 81.02 467.19
13.4 41.58 1020.5 71.17 461.54
27.1 52.84 1006.28 53.85 439.08
14.28 42.74 1028.79 70.67 467.22
16.29 44.34 1019.49 59.36 468.8
31.24 71.98 1004.66 57.17 426.93
10.57 37.73 1024.36 70.29 474.65
13.8 44.21 1022.93 83.37 468.97
25.3 71.58 1010.18 87.36 433.97
18.06 50.16 1009.52 100.09 450.53
25.42 59.04 1011.98 68.78 444.51
15.07 40.69 1015.29 70.98 469.03
11.75 71.14 1019.36 75.68 466.56
20.23 52.05 1012.15 47.49 457.57
27.31 59.54 1006.24 71.99 440.13
28.57 69.84 1003.57 66.55 433.24
17.9 43.72 1008.64 74.73 452.55
23.83 71.37 1002.04 64.78 443.29
27.92 74.99 1005.47 75.13 431.76
17.34 44.78 1007.81 56.38 454.97
17.94 63.07 1012.42 94.35 456.7
6.4 39.9 1007.75 86.55 486.03
11.78 39.96 1011.37 82.95 472.79
20.28 57.25 1010.12 88.42 452.03
21.04 54.2 1012.26 85.61 443.41
25.11 67.32 1014.49 58.39 441.93
30.28 70.98 1007.51 74.28 432.64
8.14 36.24 1013.15 87.85 480.25
16.86 39.63 1004.47 83.5 466.68
6.25 40.07 1020.19 65.24 494.39
22.35 54.42 1012.46 75.01 454.72
17.98 56.85 1012.28 84.52 448.71
21.19 42.48 1013.43 80.52 469.76
20.94 44.89 1009.64 75.14 450.71
24.23 58.79 1009.8 75.75 444.01
19.18 58.2 1017.46 76.72 453.2
20.88 57.85 1012.39 85.47 450.87
23.67 63.86 1019.67 57.95 441.73
14.12 39.52 1018.41 78.32 465.09
25.23 64.63 1020.59 52.2 447.28
6.54 39.33 1011.54 93.69 491.16
20.08 62.52 1017.99 75.74 450.98
24.67 63.56 1013.75 67.56 446.3
27.82 79.74 1008.37 69.46 436.48
15.55 42.03 1017.41 74.58 460.84
24.26 69.51 1013.43 53.23 442.56
13.45 41.49 1020.19 88.72 467.3
11.06 40.64 1021.47 96.16 479.13
24.91 52.3 1008.72 68.26 441.15
22.39 59.04 1011.78 86.39 445.52
11.95 40.69 1015.62 85.34 475.4
14.85 40.69 1014.91 72.64 469.3
10.11 41.62 1017.17 97.82 463.57
23.67 68.67 1006.71 77.22 445.32
16.14 44.21 1020.36 80.59 461.03
15.11 43.13 1014.99 46.91 466.74
24.14 59.87 1018.47 57.76 444.04
30.08 67.25 1017.6 53.09 434.01
14.77 44.9 1020.5 84.31 465.23
27.6 69.34 1009.63 71.58 440.6
13.89 44.84 1023.66 92.97 466.74
26.85 75.6 1017.43 74.55 433.48
12.41 40.96 1023.36 78.96 473.59
13.08 41.74 1020.75 64.44 474.81
18.93 44.06 1017.58 68.23 454.75
20.5 49.69 1009.6 70.81 452.94
30.72 69.13 1009.94 61.66 435.83
7.55 39.22 1014.53 77.76 482.19
13.49 44.47 1030.46 69.49 466.66
15.62 40.12 1013.03 96.26 462.59
24.8 64.63 1020.69 55.74 447.82
10.03 41.62 1014.55 95.61 462.73
22.43 63.21 1012.06 84.75 447.98
14.95 39.31 1009.15 75.3 462.72
24.78 58.46 1016.82 67.5 442.42
23.2 48.41 1008.64 80.92 444.69
14.01 39.0 1016.73 79.23 466.7
19.4 64.63 1020.38 81.1 453.84
30.15 67.32 1013.83 32.8 436.92
6.91 36.08 1021.82 84.31 486.37
29.04 60.07 1015.42 46.15 440.43
26.02 63.07 1010.94 53.96 446.82
5.89 39.48 1005.11 59.83 484.91
26.52 71.64 1008.27 75.3 437.76
28.53 68.08 1013.27 42.53 438.91
16.59 39.54 1007.97 70.58 464.19
22.95 67.79 1009.89 91.69 442.19
23.96 47.43 1008.38 63.55 446.86
17.48 44.2 1018.89 61.51 457.15
6.69 43.65 1020.14 69.55 482.57
10.25 41.26 1007.44 98.08 476.03
28.87 72.58 1008.69 79.34 428.89
12.04 40.23 1018.07 81.28 472.7
22.58 52.3 1009.04 78.99 445.6
15.12 52.05 1014.63 80.38 464.78
25.48 58.95 1017.02 51.16 440.42
27.87 70.79 1003.96 72.17 428.41
23.72 70.47 1010.65 75.39 438.5
25.0 59.43 1007.84 68.91 438.28
8.42 40.64 1022.35 96.38 476.29
22.46 58.49 1011.5 70.54 448.46
29.92 57.19 1008.62 45.8 438.99
11.68 39.22 1017.9 57.95 471.8
14.04 42.44 1012.74 81.89 471.81
19.86 59.14 1016.12 69.32 449.82
25.99 68.08 1013.13 59.14 442.14
23.42 58.79 1009.74 81.54 441.46
10.6 40.22 1011.37 85.81 477.62
20.97 61.87 1011.45 65.41 446.76
14.14 39.82 1012.46 81.15 472.52
8.56 40.71 1021.27 95.87 471.58
24.86 72.39 1001.15 90.24 440.85
29.0 77.54 1011.33 75.13 431.37
27.59 71.97 1008.64 88.22 437.33
10.45 40.71 1015.68 81.48 469.22
8.51 40.78 1023.51 89.84 471.11
29.82 66.51 1010.98 43.57 439.17
22.56 62.26 1012.11 63.16 445.33
11.38 39.22 1018.62 57.14 473.71
20.25 57.76 1016.28 77.76 452.66
22.42 59.43 1007.12 90.56 440.99
14.85 38.91 1014.48 60.98 467.42
25.62 58.82 1010.02 70.31 444.14
19.85 56.53 1020.57 74.05 457.17
13.67 54.3 1015.92 75.42 467.87
24.39 70.72 1009.78 82.25 442.04
16.07 44.58 1019.52 67.95 471.36
11.6 39.1 1009.81 100.09 460.7
31.38 70.83 1010.35 47.28 431.33
29.91 76.86 998.59 72.41 432.6
19.67 59.39 1014.07 77.67 447.61
27.18 64.79 1016.27 63.7 443.87
21.39 52.3 1009.2 79.77 446.87
10.45 41.01 1020.57 93.84 465.74
19.46 56.89 1014.02 84.95 447.86
23.55 62.96 1020.16 70.16 447.65
23.35 63.47 1011.78 84.24 437.87
9.26 41.66 1016.87 73.32 483.51
10.3 41.46 1018.21 86.17 479.65
20.94 58.16 1016.88 65.43 455.16
23.13 71.25 1002.49 94.59 431.91
12.77 41.5 1014.13 86.8 470.68
28.29 69.13 1009.29 58.18 429.28
19.13 59.21 1018.32 89.66 450.81
24.44 73.5 1011.49 87.39 437.73
20.32 44.6 1015.16 36.35 460.21
20.54 69.05 1001.6 79.62 442.86
12.16 45.0 1021.51 50.52 482.99
28.09 65.27 1013.27 51.96 440.0
9.25 41.82 1033.25 74.73 478.48
21.75 49.82 1015.01 78.33 455.28
23.7 66.56 1002.07 85.19 436.94
16.22 37.87 1022.36 83.13 461.06
24.75 69.45 1013.97 53.49 438.28
10.48 39.58 1011.81 88.86 472.61
29.53 70.79 1003.7 60.89 426.85
12.59 39.72 1017.76 61.14 470.18
23.5 54.42 1012.31 68.29 455.38
29.01 66.56 1006.44 57.62 428.32
9.75 42.49 1010.57 83.63 480.35
19.55 56.53 1020.2 78.1 455.56
21.05 58.33 1013.14 66.34 447.66
24.72 68.67 1006.74 79.02 443.06
21.19 58.86 1014.19 68.96 452.43
10.77 41.54 1019.94 71.13 477.81
28.68 73.77 1004.72 87.01 431.66
29.87 73.91 1004.53 74.3 431.8
22.99 68.67 1006.65 77.62 446.67
24.66 60.29 1018.0 59.56 445.26
32.63 69.89 1013.85 41.66 425.72
31.38 72.29 1008.73 73.27 430.58
23.87 60.27 1018.94 77.16 439.86
25.6 59.15 1013.31 67.02 441.11
27.62 71.14 1011.6 52.8 434.72
30.1 67.45 1014.23 39.04 434.01
12.19 41.17 1019.43 65.47 475.64
13.11 41.58 1020.43 74.32 460.44
28.29 68.67 1005.46 69.22 436.4
13.45 40.73 1018.7 93.88 461.03
10.98 41.54 1019.94 69.83 479.08
26.48 69.14 1009.31 84.11 435.76
13.07 45.51 1015.22 78.65 460.14
25.56 75.6 1017.37 69.31 442.2
22.68 50.78 1008.83 70.3 447.69
28.86 73.67 1006.65 68.23 431.15
22.7 63.56 1014.32 71.76 445.0
27.89 73.21 1001.32 85.88 431.59
13.78 44.47 1027.94 71.09 467.22
28.14 51.43 1012.16 52.67 445.33
11.8 45.09 1013.21 89.68 470.57
10.71 39.61 1018.72 73.66 473.77
24.54 60.29 1017.42 58.94 447.67
11.54 40.05 1014.78 87.05 474.29
29.47 71.32 1008.07 67.0 437.14
29.24 69.05 1003.12 43.18 432.56
14.51 41.79 1009.72 80.62 459.14
22.91 60.07 1016.03 59.72 446.19
27.02 71.77 1006.38 72.1 428.1
13.49 44.47 1030.18 69.15 468.46
30.24 66.75 1017.95 55.66 435.02
23.19 48.6 1002.38 61.19 445.52
17.73 40.55 1003.36 74.62 462.69
18.62 61.27 1019.26 73.35 455.75
12.85 40.0 1015.89 68.85 463.74
32.33 69.68 1011.95 39.89 439.79
25.09 58.95 1016.99 53.16 443.26
29.45 69.13 1009.3 52.97 432.04
16.91 43.96 1013.32 79.87 465.86
14.09 45.87 1009.05 84.09 465.6
10.73 25.36 1009.35 100.15 469.43
23.2 49.3 1003.4 79.77 440.75
8.21 38.91 1015.82 88.99 481.32
9.3 40.56 1022.64 76.14 479.87
16.97 39.16 1005.7 69.13 458.59
23.69 71.97 1009.62 93.03 438.62
25.13 59.44 1012.38 77.92 445.59
9.86 43.56 1015.13 74.89 481.87
11.33 41.5 1013.58 88.7 475.01
26.95 48.41 1008.53 62.94 436.54
15.0 40.66 1016.28 89.62 456.63
20.76 62.52 1015.63 81.04 451.69
14.29 39.59 1010.93 94.53 463.04
19.74 67.71 1007.68 64.02 446.1
26.68 59.92 1009.94 70.57 438.67
14.24 41.4 1019.7 70.32 466.88
21.98 48.41 1008.42 84.86 444.6
22.75 59.39 1015.4 81.41 440.26
8.34 40.96 1023.28 89.45 483.92
11.8 41.2 1017.18 82.71 475.19
8.81 44.68 1023.06 93.93 479.24
30.05 73.68 1014.95 70.6 434.92
16.01 65.46 1014.0 87.68 454.16
21.75 58.79 1012.42 87.58 447.58
13.94 41.26 1021.67 74.4 467.9
29.25 69.13 1010.27 67.35 426.29
22.33 45.87 1007.8 63.61 447.02
16.43 41.79 1005.47 76.89 455.85
11.5 40.22 1010.31 78.08 476.46
23.53 68.94 1007.53 69.17 437.48
21.86 49.21 1014.61 53.31 452.77
6.17 39.33 1012.57 93.32 491.54
30.19 64.79 1017.22 42.47 438.41
11.67 41.93 1019.81 82.58 476.1
15.34 36.99 1007.87 94.59 464.58
11.5 40.78 1023.91 86.31 467.74
25.53 57.17 1010.0 72.57 442.12
21.27 57.5 1014.53 80.76 453.34
28.37 69.13 1010.44 71.93 425.29
28.39 51.43 1011.74 47.54 449.63
13.78 45.78 1025.27 95.72 462.88
14.6 42.32 1015.71 77.03 464.67
5.1 35.57 1027.17 80.49 489.96
7.0 38.08 1020.27 77.67 482.38
26.3 77.95 1009.45 78.72 437.95
30.56 71.98 1004.74 58.77 429.2
21.09 46.63 1013.03 74.8 453.34
28.21 70.02 1010.58 51.34 442.47
15.84 49.69 1015.14 90.41 462.6
10.03 40.96 1024.57 91.1 478.79
20.37 52.05 1012.34 62.57 456.11
21.19 50.16 1005.81 84.27 450.33
33.73 69.88 1007.21 42.93 434.83
29.87 73.68 1015.1 40.96 433.43
19.62 62.96 1020.76 76.53 456.02
9.93 40.67 1018.08 69.74 485.23
9.43 37.14 1013.03 74.99 473.57
14.24 39.58 1011.17 70.45 469.94
12.97 49.83 1008.69 91.49 452.07
7.6 41.04 1021.82 88.97 475.32
8.39 36.24 1013.39 89.13 480.69
25.41 48.06 1013.12 46.52 444.01
18.43 56.03 1020.41 60.55 465.17
10.31 39.82 1012.87 88.71 480.61
11.29 41.5 1013.39 89.15 476.04
22.61 49.3 1003.51 83.02 441.76
29.34 71.98 1005.19 75.19 428.24
18.87 67.71 1004.0 87.35 444.77
13.21 45.87 1008.58 85.66 463.1
11.3 44.6 1018.19 91.66 470.5
29.23 72.99 1007.04 63.47 431.0
27.76 69.4 1004.27 72.25 430.68
29.26 67.17 1006.6 70.58 436.42
25.72 49.82 1016.19 60.1 452.33
23.43 63.94 1010.64 89.29 440.16
25.6 63.76 1010.18 67.43 435.75
22.3 44.57 1008.48 67.58 449.74
27.91 72.24 1010.74 70.8 430.73
30.35 77.17 1009.55 63.62 432.75
21.78 47.43 1007.88 66.68 446.79
7.19 41.39 1018.12 90.76 486.35
20.88 59.8 1015.66 75.34 453.18
24.19 50.23 1015.73 59.77 458.31
9.98 41.54 1019.7 80.79 480.26
23.47 51.3 1011.89 74.1 448.65
26.35 49.5 1012.67 41.34 458.41
29.89 64.69 1006.37 58.78 435.39
19.29 50.16 1010.49 97.78 450.21
17.48 43.14 1018.68 74.85 459.59
25.21 75.6 1017.19 69.84 445.84
23.3 48.78 1018.17 75.36 441.08
15.42 37.85 1009.89 85.8 467.33
21.44 63.09 1016.56 90.11 444.19
29.45 68.27 1007.96 61.63 432.96
29.69 47.93 1002.85 44.76 438.09
15.52 36.99 1006.86 89.7 467.9
11.47 43.67 1012.68 72.51 475.72
9.77 34.69 1027.72 74.98 477.51
22.6 69.84 1006.37 79.59 435.13
8.24 39.61 1017.99 78.42 477.9
17.01 44.2 1019.18 61.23 457.26
19.64 44.6 1015.88 47.56 467.53
10.61 41.58 1021.08 93.06 465.15
12.04 40.1 1014.42 89.65 474.28
29.19 65.71 1013.85 50.5 444.49
21.75 45.09 1014.15 44.84 452.84
23.66 77.54 1008.5 85.32 435.38
27.05 75.33 1003.88 82.94 433.57
29.63 69.71 1009.04 67.26 435.27
18.2 39.63 1005.35 79.05 468.49
32.22 70.8 1009.9 62.03 433.07
26.88 73.56 1004.85 94.36 430.63
29.05 65.74 1013.29 60.02 440.74
8.9 39.96 1026.31 95.46 474.49
18.93 48.6 1005.72 84.92 449.74
27.49 63.76 1010.09 62.8 436.73
23.1 70.79 1006.53 90.81 434.58
11.22 43.13 1017.24 80.9 473.93
31.97 79.74 1007.03 55.84 435.99
13.32 43.22 1009.45 75.3 466.83
31.68 68.24 1005.29 37.34 427.22
23.69 63.77 1013.39 79.5 444.07
13.83 41.49 1020.11 87.29 469.57
18.32 66.51 1015.18 81.5 459.89
11.05 40.71 1024.91 76.42 479.59
22.03 64.69 1007.21 75.75 440.92
10.23 41.46 1020.45 84.95 480.87
23.92 66.54 1009.93 62.37 441.9
29.38 69.68 1011.35 49.25 430.2
17.35 42.86 1014.62 74.16 465.16
9.81 44.45 1021.19 90.55 471.32
4.97 40.64 1020.91 94.28 485.43
5.15 40.07 1012.27 63.31 495.35
21.54 58.49 1010.85 78.9 449.12
7.94 42.02 1006.22 90.97 480.53
18.77 50.66 1014.89 87.34 457.07
21.69 69.94 1010.7 80.8 443.67
10.07 44.68 1023.44 90.95 477.52
13.83 39.64 1012.52 69.97 472.95
10.45 39.69 1003.92 89.45 472.54
11.56 40.71 1015.85 76.08 469.17
23.64 70.04 1011.09 83.35 435.21
10.48 40.22 1004.81 92.16 477.78
13.09 39.85 1012.86 58.42 475.89
10.67 40.23 1017.75 85.06 483.9
12.57 39.16 1016.53 88.91 476.2
14.45 43.34 1015.47 83.33 462.16
14.22 37.85 1011.24 88.49 471.05
6.97 41.26 1010.6 96.88 484.71
20.61 63.86 1015.43 73.86 446.34
14.67 42.28 1007.21 65.17 469.02
29.06 72.86 1004.23 69.41 432.12
14.38 40.1 1015.51 81.23 467.28
32.51 69.98 1013.29 54.07 429.66
11.79 45.09 1013.16 89.17 469.49
8.65 40.56 1023.23 78.85 485.87
9.75 40.81 1026.0 84.44 481.95
9.11 40.02 1031.1 83.02 479.03
23.39 69.13 1010.99 90.66 434.5
14.3 54.3 1015.16 75.29 464.9
17.49 63.94 1020.02 82.6 452.71
31.1 69.51 1010.84 45.4 429.74
19.77 56.65 1020.67 66.33 457.09
28.61 72.29 1011.61 45.33 446.77
13.52 41.48 1014.46 67.12 460.76
13.52 40.83 1008.31 84.14 471.95
17.57 46.21 1014.09 80.81 453.29
28.18 60.07 1016.34 49.13 441.61
14.29 46.18 1017.01 87.29 464.73
18.12 43.69 1016.91 52.95 464.68
31.27 73.91 1003.72 68.92 430.59
26.24 77.95 1014.19 85.21 438.01
7.44 41.04 1021.84 88.56 479.08
29.78 74.78 1009.28 55.09 436.39
23.37 65.46 1016.25 48.64 447.07
10.62 39.58 1011.9 87.85 479.91
5.84 43.02 1013.88 87.42 489.05
14.51 53.82 1016.46 62.75 463.17
11.31 42.02 1001.18 94.86 471.26
11.25 40.67 1011.64 63.54 480.49
9.18 39.42 1025.41 69.46 473.78
19.82 58.16 1016.76 74.66 455.5
24.77 58.41 1013.78 80.57 446.27
9.66 41.06 1021.21 84.7 482.2
21.96 59.8 1016.72 72.6 452.48
18.59 43.14 1011.92 52.63 464.48
24.75 69.89 1015.29 82.01 438.1
24.37 63.47 1012.77 75.22 445.6
29.6 67.79 1010.37 51.05 442.43
25.32 61.25 1011.56 80.1 436.67
16.15 41.85 1016.54 81.58 466.56
15.74 71.14 1019.65 65.94 457.29
5.97 36.25 1029.65 86.74 487.03
15.84 52.72 1026.45 62.57 464.93
14.84 44.63 1019.28 57.37 466.0
12.25 48.79 1017.44 88.91 469.52
27.38 70.04 1011.18 72.26 428.88
8.76 41.48 1018.49 74.98 474.3
15.54 39.31 1009.69 71.19 461.06
18.71 39.39 1014.09 62.82 465.57
13.06 41.78 1012.3 55.31 467.67
12.72 40.71 1016.02 71.57 466.99
19.83 39.39 1013.73 59.16 463.72
27.23 49.16 1004.03 40.8 443.78
24.27 68.28 1005.43 67.63 445.23
11.8 40.66 1017.13 97.2 464.43
6.76 36.25 1028.31 91.16 484.36
25.99 63.07 1012.5 64.81 442.16
16.3 39.63 1004.64 85.61 464.11
16.5 49.39 1018.35 93.42 462.48
10.59 42.49 1009.59 77.36 477.49
26.05 65.59 1012.78 67.03 437.04
19.5 40.79 1003.8 89.45 457.09
22.21 45.01 1012.22 54.84 450.6
17.86 45.0 1023.25 53.48 465.78
29.96 70.04 1010.15 54.47 427.1
19.08 44.63 1020.14 43.36 459.81
23.59 47.43 1006.64 48.92 447.36
3.38 39.64 1011.0 81.22 488.92
26.39 66.49 1012.96 60.35 433.36
8.99 39.04 1021.99 75.98 483.35
10.91 41.04 1026.57 74.24 469.53
13.08 39.82 1012.27 85.21 476.96
23.95 58.46 1017.5 68.46 440.75
15.64 43.71 1024.51 78.31 462.55
18.78 54.2 1012.05 89.25 448.04
20.65 50.59 1016.22 68.57 455.24
4.96 40.07 1011.8 67.38 494.75
23.51 57.32 1012.55 53.6 444.58
5.99 35.79 1011.56 91.69 484.82
23.65 66.05 1019.6 78.21 442.9
5.17 39.33 1009.68 94.19 485.46
26.38 49.5 1012.82 37.19 457.81
6.02 43.65 1013.85 83.53 481.92
23.2 61.02 1009.63 79.45 443.23
8.57 39.69 1000.91 99.9 474.29
30.72 71.58 1009.98 50.39 430.46
21.52 50.66 1013.56 74.33 455.71
22.93 62.26 1011.25 83.66 438.34
5.71 41.31 1003.24 89.48 485.83
18.62 44.06 1017.76 64.59 452.82
27.88 68.94 1007.68 75.68 435.04
22.32 59.8 1016.82 64.18 451.21
14.55 42.74 1028.41 70.09 465.81
17.83 44.92 1025.04 70.58 458.42
9.68 39.96 1026.09 99.28 470.22
19.41 49.39 1020.84 81.89 449.24
13.22 44.92 1023.84 87.99 471.43
12.24 44.92 1023.74 88.21 473.26
19.21 58.49 1011.7 91.29 452.82
29.74 70.32 1008.1 52.72 432.69
23.28 60.84 1017.91 67.5 444.13
8.02 41.92 1029.8 92.05 467.21
22.47 48.6 1002.33 63.23 445.98
27.51 73.77 1002.42 90.88 436.91
17.51 44.9 1009.05 74.91 455.01
23.22 66.56 1002.47 85.39 437.11
11.73 40.64 1020.68 96.98 477.06
21.19 67.71 1006.65 56.28 441.71
5.48 40.07 1019.63 65.62 495.76
24.26 66.44 1011.33 55.32 445.63
12.32 41.62 1012.88 88.88 464.72
31.26 68.94 1005.94 39.49 438.03
32.09 72.86 1003.47 54.59 434.78
24.98 60.32 1015.63 57.19 444.67
27.48 61.41 1012.2 45.06 452.24
21.04 45.09 1014.19 40.62 450.92
27.75 70.4 1006.65 90.21 436.53
22.79 71.77 1005.75 90.91 435.53
24.22 68.51 1013.23 74.96 440.01
27.06 64.45 1008.72 54.21 443.1
29.25 71.94 1007.18 63.62 427.49
26.86 68.08 1012.99 50.04 436.25
29.64 67.79 1009.99 51.23 440.74
19.92 63.31 1015.02 82.71 443.54
18.5 51.43 1010.82 92.04 459.42
23.71 60.23 1009.76 90.67 439.66
14.39 44.84 1023.55 91.14 464.15
19.3 56.65 1020.55 70.43 459.1
24.65 52.36 1014.76 66.63 455.68
13.5 45.51 1015.33 86.95 469.08
9.82 41.26 1007.71 96.69 478.02
18.4 44.06 1017.36 70.88 456.8
28.12 44.89 1009.18 47.14 441.13
17.15 43.69 1017.05 63.36 463.88
30.69 73.67 1006.14 60.58 430.45
28.82 65.71 1014.24 54.3 449.18
21.3 48.92 1010.92 65.09 447.89
30.58 70.04 1010.4 48.16 431.59
21.17 52.3 1009.36 81.51 447.5
9.87 41.82 1033.04 68.57 475.58
22.18 59.8 1016.77 73.16 453.24
24.39 63.21 1012.59 80.88 446.4
10.73 44.92 1025.1 85.4 476.81
9.38 40.46 1019.29 75.77 474.1
20.27 57.76 1016.66 75.76 450.71
24.82 66.48 1006.4 70.21 433.62
16.55 41.66 1011.45 55.53 465.14
20.73 59.87 1019.08 80.48 445.18
9.51 39.22 1015.3 72.41 474.12
8.63 43.79 1016.08 83.25 483.91
6.48 40.27 1010.55 82.12 486.68
14.95 43.52 1022.43 94.75 464.98
5.76 45.87 1010.83 95.79 481.4
10.94 39.04 1021.81 86.02 479.2
15.87 41.16 1005.85 78.29 463.86
12.42 38.25 1012.76 82.23 472.3
29.12 58.84 1001.31 52.86 446.51
29.12 51.43 1005.93 60.66 437.71
19.08 41.1 1001.96 62.77 458.94
31.06 67.17 1007.62 65.54 437.91
5.72 39.33 1009.96 95.4 490.76
26.52 65.06 1013.4 51.78 439.66
13.84 44.9 1007.58 63.62 463.27
13.03 39.52 1016.68 83.09 473.99
25.94 66.49 1012.83 61.81 433.38
16.64 53.82 1015.13 68.24 459.01
14.13 40.75 1016.05 72.41 471.44
13.65 39.28 1012.97 79.64 471.91
14.5 44.47 1028.2 66.95 465.15
19.8 51.19 1008.25 91.98 446.66
25.2 63.76 1009.78 64.96 438.15
20.66 51.19 1008.81 88.93 447.14
12.07 43.71 1025.53 85.62 472.32
25.64 70.72 1010.16 84.0 441.68
23.33 72.99 1009.33 89.41 440.04
29.41 64.05 1009.82 67.4 444.82
16.6 53.16 1014.5 76.75 457.26
27.53 72.58 1009.13 89.06 428.83
20.62 43.43 1009.93 64.02 449.07
26.02 71.94 1009.38 64.12 435.21
12.75 44.2 1017.59 81.22 471.03
12.87 48.04 1012.47 100.13 465.56
25.77 62.96 1019.86 58.07 442.83
14.84 41.48 1017.26 63.42 460.3
7.41 40.71 1023.07 83.32 474.25
8.87 41.82 1033.3 74.28 477.97
9.69 40.46 1019.1 71.91 472.16
16.17 46.97 1014.22 85.8 456.08
26.24 49.82 1014.9 55.58 452.41
13.78 43.22 1011.31 69.7 463.71
26.3 67.07 1006.26 63.79 433.72
17.37 57.76 1016.0 86.59 456.4
23.6 48.98 1015.41 48.28 448.43
8.3 36.08 1020.63 80.42 481.6
18.86 42.18 1001.16 98.58 457.07
22.12 49.39 1019.8 72.83 451.0
28.41 75.6 1018.48 56.07 440.28
29.42 71.32 1002.26 67.13 437.47
18.61 67.71 1004.07 84.49 443.57
27.57 69.84 1004.91 68.37 426.6
12.83 41.5 1013.12 86.07 470.87
9.64 39.85 1012.9 83.82 478.37
19.13 58.66 1013.32 74.86 453.92
15.92 40.56 1020.79 53.52 470.22
24.64 72.24 1011.37 80.61 434.54
27.62 63.9 1013.11 43.56 442.89
8.9 36.24 1013.29 89.35 479.03
9.55 43.99 1020.5 97.28 476.06
10.57 36.71 1022.62 80.49 473.88
19.8 57.25 1010.84 88.9 451.75
25.63 56.85 1012.68 49.7 439.2
24.7 58.46 1015.58 68.64 439.7
15.26 46.18 1013.68 98.58 463.6
20.06 52.84 1004.21 82.12 447.47
19.84 56.89 1013.23 78.32 447.92
11.49 44.63 1020.44 86.04 471.08
23.74 72.43 1007.99 91.36 437.55
22.62 51.3 1012.36 81.02 448.27
29.53 72.39 998.47 76.05 431.69
21.32 48.14 1016.57 71.81 449.09
20.3 58.46 1015.93 82.13 448.79
16.97 44.92 1025.21 74.27 460.21
12.07 41.17 1013.54 71.32 479.28
7.46 41.82 1032.67 74.59 483.11
19.2 54.2 1011.46 84.44 450.75
28.64 66.54 1010.43 43.39 437.97
13.56 41.48 1008.53 87.2 459.76
17.4 44.9 1020.5 77.11 457.75
14.08 40.1 1015.48 82.81 469.33
27.11 69.75 1009.74 85.67 433.28
20.92 70.02 1010.23 95.58 444.64
16.18 44.9 1021.3 74.46 463.1
15.57 44.68 1022.01 90.02 460.91
10.37 39.04 1023.95 81.93 479.35
19.6 59.21 1017.65 86.29 449.23
9.22 40.92 1021.83 85.43 474.51
27.76 72.99 1007.81 71.66 435.02
28.68 70.72 1009.43 71.33 435.45
20.95 48.14 1013.3 67.72 452.38
9.06 39.3 1019.73 84.23 480.41
9.21 39.72 1019.54 74.44 478.96
13.65 42.74 1026.58 71.48 468.87
31.79 76.2 1007.89 56.3 434.01
14.32 44.6 1013.85 68.13 466.36
26.28 75.23 1011.44 68.35 435.28
7.69 43.02 1014.51 85.23 486.46
14.44 40.1 1015.51 79.78 468.19
9.19 41.01 1022.14 98.98 468.37
13.35 41.39 1019.17 72.87 474.19
23.04 74.22 1009.52 90.93 440.32
4.83 38.44 1015.35 72.94 485.32
17.29 42.86 1014.38 72.3 464.27
8.73 36.18 1013.66 77.74 479.25
26.21 70.32 1007.0 78.29 430.4
23.72 58.62 1016.65 69.1 447.49
29.27 64.69 1006.85 55.79 438.23
10.4 40.43 1025.46 75.09 492.09
12.19 40.75 1015.13 88.98 475.36
20.4 54.9 1016.68 64.26 452.56
34.3 74.67 1015.98 25.89 427.84
27.56 68.08 1010.8 59.18 433.95
30.9 70.8 1008.48 67.48 435.27
14.85 58.59 1014.04 89.85 454.62
16.42 40.56 1020.36 50.62 472.17
16.45 63.31 1015.96 83.97 452.42
10.14 42.02 1003.19 96.51 472.17
9.53 41.44 1018.01 80.09 481.83
17.01 49.15 1021.83 84.02 458.78
23.94 62.08 1022.47 61.97 447.5
15.95 49.25 1019.04 88.51 463.4
11.15 41.26 1022.67 81.83 473.57
25.56 70.32 1009.07 90.63 433.72
27.16 66.44 1011.2 73.37 431.85
26.71 77.95 1012.13 77.5 433.47
29.56 74.22 1007.45 57.46 432.84
31.19 70.94 1007.29 51.91 436.6
6.86 41.17 1020.12 79.14 490.23
12.36 41.74 1020.58 69.24 477.16
32.82 68.31 1010.44 41.85 441.06
25.3 70.98 1007.22 95.1 440.86
8.71 41.82 1033.08 74.53 477.94
13.34 40.8 1026.56 64.85 474.47
14.2 43.02 1012.18 57.07 470.67
23.74 65.34 1013.7 62.9 447.31
16.9 44.88 1018.14 72.21 466.8
28.54 71.94 1007.4 65.99 430.91
30.15 69.88 1007.2 73.67 434.75
14.33 42.86 1010.82 88.59 469.52
25.57 59.43 1008.88 61.19 438.9
30.55 70.04 1010.51 49.37 429.56
28.04 74.33 1013.53 48.65 432.92
26.39 49.16 1005.68 56.18 442.87
15.3 41.76 1022.57 71.56 466.59
6.03 41.14 1028.04 87.46 479.61
13.49 44.63 1019.12 70.02 471.08
27.67 59.14 1016.51 61.2 433.37
24.19 65.48 1018.8 60.54 443.92
24.44 59.14 1016.74 71.82 443.5
29.86 64.79 1017.37 44.8 439.89
30.2 69.59 1008.9 67.32 434.66
7.99 41.38 1021.95 78.77 487.57
9.93 41.62 1013.76 96.02 464.64
11.03 42.32 1017.26 90.56 470.92
22.34 63.73 1014.37 83.19 444.39
25.33 48.6 1002.54 68.45 442.48
18.87 52.08 1005.25 99.19 449.61
25.97 69.34 1009.43 88.11 435.02
16.58 43.99 1021.81 79.29 458.67
14.35 46.18 1016.63 87.76 461.74
25.06 62.39 1008.09 82.56 438.31
13.85 48.92 1011.68 79.24 462.38
16.09 44.2 1019.39 67.24 460.56
26.34 59.21 1013.37 58.98 439.22
23.01 58.79 1009.71 84.22 444.64
26.39 71.25 999.8 89.12 430.34
31.32 71.29 1008.37 50.07 430.46
16.64 45.87 1009.02 98.86 456.79
13.42 41.23 994.17 95.79 468.82
20.06 44.9 1008.79 70.06 448.51
14.8 44.71 1014.67 41.71 470.77
12.59 41.14 1025.79 86.55 465.74
26.7 66.56 1005.31 71.97 430.21
19.78 50.32 1008.62 96.4 449.23
15.17 49.15 1021.91 91.73 461.89
21.71 61.45 1010.97 91.62 445.72
19.09 39.39 1013.36 59.14 466.13
19.76 51.19 1008.38 92.56 448.71
14.68 41.23 998.43 83.71 469.25
21.3 66.86 1013.04 55.43 450.56
16.73 39.64 1008.94 74.91 464.46
12.26 41.5 1014.87 89.41 471.13
14.77 48.06 1010.92 69.81 461.52
18.26 59.15 1012.04 86.01 451.09
27.1 79.74 1005.43 86.05 431.51
14.72 40.83 1009.65 80.98 469.8
26.3 51.43 1012.05 63.62 442.28
16.48 48.92 1011.84 64.16 458.67
17.99 43.79 1016.13 75.63 462.4
20.34 59.8 1015.18 80.21 453.54
25.53 62.96 1019.81 59.7 444.38
31.59 58.9 1003.39 47.6 440.52
30.8 69.14 1007.68 63.78 433.62
10.75 45.0 1023.68 89.37 481.96
19.3 44.9 1008.89 70.55 452.75
4.71 39.42 1026.4 84.42 481.28
23.1 66.05 1020.28 80.62 439.03
32.63 73.88 1005.64 52.56 435.75
26.63 74.16 1009.72 83.26 436.03
24.35 58.49 1011.03 70.64 445.6
15.11 56.03 1020.27 89.95 462.65
29.1 50.05 1005.87 51.53 438.66
21.24 50.32 1008.54 84.83 447.32
6.16 39.48 1004.85 59.68 484.55
7.36 41.01 1024.9 97.88 476.8
10.44 39.04 1023.99 85.03 480.34
26.76 48.41 1010.53 47.38 440.63
16.79 44.6 1014.27 48.08 459.48
10.76 40.43 1025.98 79.65 490.78
6.07 38.91 1019.25 83.39 483.56
27.33 73.18 1012.26 82.18 429.38
27.15 59.21 1013.49 51.71 440.27
22.35 51.43 1011.34 77.33 445.34
21.82 65.27 1013.86 72.81 447.43
21.11 69.94 1004.37 84.26 439.91
19.95 50.59 1016.11 73.23 459.27
7.45 39.61 1017.88 79.73 478.89
15.36 41.66 1012.41 62.32 466.7
15.65 43.5 1021.39 78.58 463.5
25.31 74.33 1015.04 79.88 436.21
25.88 63.47 1011.95 65.87 443.94
24.6 63.94 1012.87 80.28 439.63
22.58 41.54 1013.21 71.33 460.95
19.69 59.14 1015.99 70.33 448.69
25.85 75.08 1006.24 57.73 444.63
10.06 37.83 1005.49 99.46 473.51
18.59 39.54 1008.56 68.61 462.56
18.27 50.16 1011.07 95.91 451.76
8.85 40.43 1025.68 80.42 491.81
30.04 68.08 1011.04 51.01 429.52
26.06 49.02 1007.59 74.08 437.9
14.8 38.73 1003.18 80.73 467.54
23.93 64.45 1015.35 54.71 449.97
23.72 66.48 1003.61 73.75 436.62
11.44 40.55 1023.37 88.43 477.68
20.28 63.86 1016.04 74.66 447.26
27.9 63.13 1011.8 70.04 439.76
24.74 59.39 1015.23 74.64 437.49
14.8 58.2 1018.29 85.11 455.14
8.22 41.03 1021.76 82.97 485.5
27.56 66.93 1016.81 55.59 444.1
32.07 70.94 1006.91 49.9 432.33
9.53 44.03 1008.87 89.99 471.23
13.61 42.34 1017.93 91.61 463.89
22.2 51.19 1009.2 82.95 445.54
21.36 59.54 1007.99 92.62 446.09
23.25 63.86 1017.82 59.64 445.12
23.5 59.21 1018.29 63.0 443.31
8.46 39.66 1015.14 85.38 484.16
8.19 40.69 1019.86 85.23 477.76
30.67 71.29 1008.36 52.08 430.28
32.48 62.04 1010.39 38.05 446.48
8.99 36.66 1028.11 71.98 481.03
13.77 47.83 1007.41 90.66 466.07
19.05 67.32 1013.2 83.14 447.47
21.19 55.5 1019.83 65.22 455.93
10.12 40.0 1021.15 91.67 479.62
24.93 47.01 1014.28 66.04 455.06
8.47 40.46 1019.87 78.19 475.06
24.52 56.85 1012.59 54.47 438.89
28.55 69.84 1003.38 67.26 432.7
20.58 50.9 1011.89 72.56 452.6
18.31 46.21 1010.46 82.15 451.75
27.18 71.06 1008.16 86.32 430.66
4.43 38.91 1019.04 88.17 491.9
26.02 74.78 1010.04 72.78 439.82
15.75 39.0 1015.91 69.58 460.73
22.99 60.95 1015.14 69.86 449.7
25.52 59.15 1013.88 65.37 439.42
27.04 65.06 1013.33 52.37 439.84
6.42 35.57 1025.58 79.63 485.86
17.04 40.12 1011.81 83.14 458.1
10.79 39.82 1012.89 88.25 479.92
20.41 56.03 1019.94 55.85 458.29
7.36 40.07 1017.29 52.55 489.45
28.08 73.42 1012.17 62.74 434.0
24.74 69.13 1010.69 90.08 431.24
28.32 47.93 1003.26 54.5 439.5
16.71 40.56 1019.48 49.88 467.46
30.7 71.58 1010.0 48.96 429.27
18.42 58.95 1016.95 86.77 452.1
10.62 42.02 999.83 96.66 472.41
22.18 69.05 1002.75 70.84 442.14
22.38 49.3 1003.56 83.83 441.0
13.94 41.58 1020.76 68.22 463.07
21.24 60.84 1017.99 82.22 445.71
6.76 39.81 1017.11 87.9 483.16
26.73 68.84 1010.75 66.83 440.45
7.24 38.06 1020.6 85.36 481.83
10.84 40.62 1015.53 60.9 467.6
19.32 52.84 1004.29 83.51 450.88
29.0 69.13 1001.22 52.96 425.5
23.38 54.42 1013.95 73.02 451.87
31.17 69.51 1010.51 43.11 428.94
26.17 48.6 1002.59 61.41 439.86
30.9 73.42 1011.21 65.32 433.44
24.92 73.68 1015.12 93.68 438.23
32.77 71.32 1007.68 42.39 436.95
14.37 40.56 1021.67 68.18 470.19
8.36 40.22 1011.6 89.18 484.66
31.45 68.27 1007.56 64.79 430.81
31.6 73.17 1010.05 43.48 433.37
17.9 48.98 1014.17 80.4 453.02
20.35 50.9 1012.6 72.43 453.5
16.21 41.23 995.88 80.0 463.09
19.36 44.6 1016.25 45.65 464.56
21.04 65.46 1017.22 63.02 452.12
14.05 40.69 1015.66 74.39 470.9
23.48 64.15 1021.08 57.77 450.89
21.91 63.76 1009.85 76.8 445.04
24.42 63.07 1011.49 67.39 444.72
14.26 40.92 1022.07 73.96 460.38
21.38 58.33 1013.05 72.75 446.8
15.71 44.06 1018.34 71.69 465.05
5.78 40.62 1016.55 84.98 484.13
6.77 39.81 1017.01 87.68 488.27
23.84 49.21 1013.85 50.36 447.09
21.17 58.16 1017.16 68.11 452.02
19.94 58.96 1014.16 66.27 455.55
8.73 41.92 1029.41 89.72 480.99
16.39 41.67 1012.96 61.07 467.68

Linear Regression Model

  • Linear Regression is one of the most useful work-horses of statistical learning
  • See Chapter 7 of Kevin Murphy's Machine Learning froma Probabilistic Perspective for a good mathematical and algorithmic introduction.
  • You should have already seen Ameet's treatment of the topic from earlier notebook.
// First let's hold out 20% of our data for testing and leave 80% for training
var Array(split20, split80) = dataset.randomSplit(Array(0.20, 0.80), 1800009193L)
split20: org.apache.spark.sql.Dataset[org.apache.spark.sql.Row] = [AT: double, V: double ... 3 more fields]
split80: org.apache.spark.sql.Dataset[org.apache.spark.sql.Row] = [AT: double, V: double ... 3 more fields]
// Let's cache these datasets for performance
val testSet = split20.cache()
val trainingSet = split80.cache()
testSet: org.apache.spark.sql.Dataset[org.apache.spark.sql.Row] = [AT: double, V: double ... 3 more fields]
trainingSet: org.apache.spark.sql.Dataset[org.apache.spark.sql.Row] = [AT: double, V: double ... 3 more fields]
testSet.count() // action to actually cache
res87: Long = 1856
trainingSet.count() // action to actually cache
res88: Long = 7712

Let's take a few elements of the three DataFrames.

dataset.take(3)
res89: Array[org.apache.spark.sql.Row] = Array([14.96,41.76,1024.07,73.17,463.26], [25.18,62.96,1020.04,59.08,444.37], [5.11,39.4,1012.16,92.14,488.56])
testSet.take(3)
res90: Array[org.apache.spark.sql.Row] = Array([2.34,39.42,1028.47,69.68,490.34], [2.8,39.64,1011.01,82.96,482.66], [3.82,35.47,1016.62,84.34,489.04])
trainingSet.take(3)
res91: Array[org.apache.spark.sql.Row] = Array([1.81,39.42,1026.92,76.97,490.55], [2.58,39.42,1028.68,69.03,488.69], [2.64,39.64,1011.02,85.24,481.29])
// ***** LINEAR REGRESSION MODEL ****

import org.apache.spark.ml.regression.LinearRegression
import org.apache.spark.ml.regression.LinearRegressionModel
import org.apache.spark.ml.Pipeline

// Let's initialize our linear regression learner
val lr = new LinearRegression()
import org.apache.spark.ml.regression.LinearRegression
import org.apache.spark.ml.regression.LinearRegressionModel
import org.apache.spark.ml.Pipeline
lr: org.apache.spark.ml.regression.LinearRegression = linReg_3b8dffe4015f
// We use explain params to dump the parameters we can use
lr.explainParams()
res92: String =
aggregationDepth: suggested depth for treeAggregate (>= 2) (default: 2)
elasticNetParam: the ElasticNet mixing parameter, in range [0, 1]. For alpha = 0, the penalty is an L2 penalty. For alpha = 1, it is an L1 penalty (default: 0.0)
epsilon: The shape parameter to control the amount of robustness. Must be > 1.0. (default: 1.35)
featuresCol: features column name (default: features)
fitIntercept: whether to fit an intercept term (default: true)
labelCol: label column name (default: label)
loss: The loss function to be optimized. Supported options: squaredError, huber. (Default squaredError) (default: squaredError)
maxIter: maximum number of iterations (>= 0) (default: 100)
predictionCol: prediction column name (default: prediction)
regParam: regularization parameter (>= 0) (default: 0.0)
solver: The solver algorithm for optimization. Supported options: auto, normal, l-bfgs. (Default auto) (default: auto)
standardization: whether to standardize the training features before fitting the model (default: true)
tol: the convergence tolerance for iterative algorithms (>= 0) (default: 1.0E-6)
weightCol: weight column name. If this is not set or empty, we treat all instance weights as 1.0 (undefined)

The cell below is based on the Spark ML pipeline API. More information can be found in the Spark ML Programming Guide at https://spark.apache.org/docs/latest/ml-guide.html

// Now we set the parameters for the method
lr.setPredictionCol("Predicted_PE")
  .setLabelCol("PE")
  .setMaxIter(100)
  .setRegParam(0.1)
// We will use the new spark.ml pipeline API. If you have worked with scikit-learn this will be very familiar.
val lrPipeline = new Pipeline()
lrPipeline.setStages(Array(vectorizer, lr))
// Let's first train on the entire dataset to see what we get
val lrModel = lrPipeline.fit(trainingSet)
lrPipeline: org.apache.spark.ml.Pipeline = pipeline_07136143d91d
lrModel: org.apache.spark.ml.PipelineModel = pipeline_07136143d91d

Since Linear Regression is simply a line of best fit over the data that minimizes the square of the error, given multiple input dimensions we can express each predictor as a line function of the form:

\[ y = b_0 + b_1 x_1 + b_2 x_2 + b_3 x_3 + \ldots + b_i x_i + \ldots + b_k x_k \]

where \(b_0\) is the intercept and \(b_i\)'s are coefficients.

To express the coefficients of that line we can retrieve the Estimator stage from the fitted, linear-regression pipeline model named lrModel and express the weights and the intercept for the function.

// The intercept is as follows:
val intercept = lrModel.stages(1).asInstanceOf[LinearRegressionModel].intercept
intercept: Double = 434.0183482461227
// The coefficents (i.e. weights) are as follows:

val weights = lrModel.stages(1).asInstanceOf[LinearRegressionModel].coefficients.toArray
weights: Array[Double] = Array(-1.9288465830313846, -0.24931659465920197, 0.08140785421485836, -0.1458797521995801)

The model has been fit and the intercept and coefficients displayed above.

Now, let us do some work to make a string of the model that is easy to understand for an applied data scientist or data analyst.

val featuresNoLabel = dataset.columns.filter(col => col != "PE")
featuresNoLabel: Array[String] = Array(AT, V, AP, RH)
val coefficentFeaturePairs = sc.parallelize(weights).zip(sc.parallelize(featuresNoLabel))
coefficentFeaturePairs: org.apache.spark.rdd.RDD[(Double, String)] = ZippedPartitionsRDD2[32671] at zip at command-2972105651606305:1
coefficentFeaturePairs.collect() // this just pairs each coefficient with the name of its corresponding feature
res93: Array[(Double, String)] = Array((-1.9288465830313846,AT), (-0.24931659465920197,V), (0.08140785421485836,AP), (-0.1458797521995801,RH))
// Now let's sort the coefficients from the largest to the smallest

var equation = s"y = $intercept "
//var variables = Array
coefficentFeaturePairs.sortByKey().collect().foreach({
  case (weight, feature) =>
  { 
        val symbol = if (weight > 0) "+" else "-"
        val absWeight = Math.abs(weight)
        equation += (s" $symbol (${absWeight} * ${feature})")
  }
}
)
equation: String = y = 434.0183482461227  - (1.9288465830313846 * AT) - (0.24931659465920197 * V) - (0.1458797521995801 * RH) + (0.08140785421485836 * AP)
// Finally here is our equation
println("Linear Regression Equation: " + equation)
Linear Regression Equation: y = 434.0183482461227  - (1.9288465830313846 * AT) - (0.24931659465920197 * V) - (0.1458797521995801 * RH) + (0.08140785421485836 * AP)

Based on examining the fitted Linear Regression Equation above:

  • There is a strong negative correlation between Atmospheric Temperature (AT) and Power Output due to the coefficient being greater than -1.91.
  • But our other dimenensions seem to have little to no correlation with Power Output.

Do you remember Step 2: Explore Your Data? When we visualized each predictor against Power Output using a Scatter Plot, only the temperature variable seemed to have a linear correlation with Power Output so our final equation seems logical.

Now let's see what our predictions look like given this model.

val predictionsAndLabels = lrModel.transform(testSet)

display(predictionsAndLabels.select("AT", "V", "AP", "RH", "PE", "Predicted_PE"))
AT V AP RH PE Predicted_PE
2.34 39.42 1028.47 69.68 490.34 493.23742177145215
2.8 39.64 1011.01 82.96 482.66 488.93663844863084
3.82 35.47 1016.62 84.34 489.04 488.2642491377776
3.98 35.47 1017.22 86.53 489.64 487.68500173970443
4.23 38.44 1016.46 76.64 489.0 487.8432005878593
4.32 35.47 1017.8 88.51 488.03 486.7875685475632
4.43 38.91 1019.04 88.17 491.9 485.8682911927764
4.65 35.19 1018.23 94.78 489.36 485.34119715268844
4.78 42.85 1013.39 93.36 481.47 482.9938172155284
4.87 42.85 1012.69 94.72 482.05 482.5648390621137
4.96 40.07 1011.8 67.38 494.75 487.00024243767876
4.97 42.85 1014.02 88.78 482.98 483.3467525779819
5.01 39.4 1003.69 91.9 475.34 482.8336530053327
5.06 40.64 1021.49 93.7 483.73 483.6145343498689
5.15 35.19 1018.63 93.94 488.42 484.53187599470635
5.15 40.07 1012.27 63.31 495.35 487.2657538698361
5.17 35.57 1026.68 79.86 491.32 487.10787889447494
5.21 41.31 1003.51 91.23 486.46 482.0547750131424
5.23 40.78 1025.13 92.74 483.12 483.688095258955
5.25 40.07 1019.48 67.7 495.23 487.0194077282659
5.28 45.87 1008.25 97.88 479.91 480.1986449575354
5.29 41.38 1020.62 83.83 492.12 484.35541367676683
5.42 41.38 1020.77 86.02 491.38 483.7973981417879
5.47 40.62 1018.66 83.61 481.56 484.07023605498495
5.51 41.03 1022.28 84.5 491.84 484.05572584065357
5.53 35.79 1011.19 94.01 484.64 483.0334383183464
5.54 41.38 1020.47 82.91 490.07 483.9952002249004
5.54 45.87 1008.69 95.91 478.02 480.02034741363497
5.56 45.87 1006.99 96.48 476.61 479.7602256710553
5.65 40.72 1022.46 85.17 487.09 483.7798894431585
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21.44 63.09 1016.56 90.11 444.19 446.545237358833
21.45 45.09 1013.83 52.26 453.15 456.3129527756159
21.45 60.08 1017.92 72.7 451.49 449.9268730104538
21.45 66.05 1014.81 73.73 453.38 448.0350183689646
21.46 46.63 1012.97 71.29 452.1 453.06361431502756
21.47 58.79 1017.0 76.97 446.33 449.51211271813366
21.49 56.9 1007.47 66.66 452.46 450.672947544889
21.52 66.51 1015.32 72.85 444.87 447.9552056621943
21.53 52.84 1005.06 88.22 444.04 448.2666586698033
21.54 58.49 1010.85 78.9 449.12 448.66968221055265
21.54 69.48 1011.04 80.48 443.15 445.7146703190735
21.55 44.57 1006.03 71.54 446.84 452.8021698612517
21.55 60.27 1017.42 92.59 443.93 446.7443660008083
21.57 66.49 1014.76 68.19 455.18 448.49796091182566
21.58 63.87 1015.27 63.15 451.88 449.90863388073797
21.61 41.54 1014.5 75.62 458.47 453.53620348431275
21.61 49.39 1019.41 78.2 449.26 451.60241101975805
21.62 50.05 1007.2 92.9 444.16 448.28015134415546
21.65 58.18 1008.33 95.28 441.05 445.940139097113
21.69 44.57 1005.84 71.53 447.88 452.5181226448485
21.71 65.27 1013.24 63.58 444.91 449.080854354919
21.73 69.05 1001.31 86.64 439.01 443.764677908941
21.75 59.8 1016.65 72.94 453.17 449.2796285666682

Now that we have real predictions we can use an evaluation metric such as Root Mean Squared Error to validate our regression model. The lower the Root Mean Squared Error, the better our model.

//Now let's compute some evaluation metrics against our test dataset

import org.apache.spark.mllib.evaluation.RegressionMetrics 

val metrics = new RegressionMetrics(predictionsAndLabels.select("Predicted_PE", "PE").rdd.map(r => (r(0).asInstanceOf[Double], r(1).asInstanceOf[Double])))
import org.apache.spark.mllib.evaluation.RegressionMetrics
metrics: org.apache.spark.mllib.evaluation.RegressionMetrics = org.apache.spark.mllib.evaluation.RegressionMetrics@2cb97126
val rmse = metrics.rootMeanSquaredError
rmse: Double = 4.426730543741181
val explainedVariance = metrics.explainedVariance
explainedVariance: Double = 269.3177257387032
val r2 = metrics.r2
r2: Double = 0.9314313152952873
println (f"Root Mean Squared Error: $rmse")
println (f"Explained Variance: $explainedVariance")  
println (f"R2: $r2")
Root Mean Squared Error: 4.426730543741181
Explained Variance: 269.3177257387032
R2: 0.9314313152952873

Generally a good model will have 68% of predictions within 1 RMSE and 95% within 2 RMSE of the actual value. Let's calculate and see if our RMSE meets this criteria.

display(predictionsAndLabels) // recall the DataFrame predictionsAndLabels
// First we calculate the residual error and divide it by the RMSE from predictionsAndLabels DataFrame and make another DataFrame that is registered as a temporary table Power_Plant_RMSE_Evaluation
predictionsAndLabels.selectExpr("PE", "Predicted_PE", "PE - Predicted_PE AS Residual_Error", s""" (PE - Predicted_PE) / $rmse AS Within_RSME""").createOrReplaceTempView("Power_Plant_RMSE_Evaluation")
SELECT * from Power_Plant_RMSE_Evaluation
PE Predicted_PE Residual_Error Within_RSME
490.34 493.23742177145215 -2.897421771452173 -0.6545286058914855
482.66 488.93663844863084 -6.27663844863082 -1.4178948518800556
489.04 488.2642491377776 0.7757508622224236 0.17524239493619823
489.64 487.68500173970443 1.9549982602955538 0.44163480044197995
489.0 487.8432005878593 1.1567994121406855 0.26132139752130357
488.03 486.7875685475632 1.24243145243679 0.28066570579802425
491.9 485.8682911927764 6.031708807223595 1.3625651590092023
489.36 485.34119715268844 4.018802847311576 0.9078489886839033
481.47 482.9938172155284 -1.5238172155283678 -0.3442308494884213
482.05 482.5648390621137 -0.5148390621137082 -0.11630232674577932
494.75 487.00024243767876 7.749757562321236 1.7506729821805804
482.98 483.3467525779819 -0.3667525779818561 -8.284953745386567e-2
475.34 482.8336530053327 -7.493653005332703 -1.692818871916148
483.73 483.6145343498689 0.11546565013111376 2.608373132048146e-2
488.42 484.53187599470635 3.888124005293662 0.8783285919200484
495.35 487.2657538698361 8.084246130163933 1.8262340682999108
491.32 487.10787889447494 4.212121105525057 0.9515196517846441
486.46 482.0547750131424 4.405224986857604 0.9951418870719423
483.12 483.688095258955 -0.5680952589549975 -0.12833292050229034
495.23 487.0194077282659 8.210592271734129 1.8547757064958097
479.91 480.1986449575354 -0.2886449575353822 -6.520499829010114e-2
492.12 484.35541367676683 7.764586323233175 1.7540228045303743
491.38 483.7973981417879 7.582601858212115 1.712912449331917
481.56 484.07023605498495 -2.5102360549849436 -0.567063215206105
491.84 484.05572584065357 7.78427415934641 1.758470293691663
484.64 483.0334383183464 1.6065616816536021 0.36292285373571487
490.07 483.9952002249004 6.0747997750996205 1.3722994239368362
478.02 480.02034741363497 -2.0003474136349837 -0.4518791902667791
476.61 479.7602256710553 -3.1502256710552956 -0.711637096481805
487.09 483.7798894431585 3.3101105568414937 0.7477551488923485
482.82 483.2217349280458 -0.401734928045812 -9.075206274161249e-2
481.6 480.1171178824119 1.482882117588133 0.33498359634397323
470.02 482.0478125504672 -12.027812550467218 -2.717087121436152
489.05 481.81327159305386 7.236728406946156 1.6347795140090344
487.03 484.6333949755666 2.39660502443337 0.5413939250993844
490.57 482.2826790358646 8.287320964135404 1.8721087453250556
488.57 482.86050781997415 5.709492180025848 1.2897763086344445
480.39 483.17821215232124 -2.7882121523212504 -0.6298581141929721
481.37 483.0829476732433 -1.7129476732433204 -0.3869554869711247
489.62 482.71830544679335 6.901694553206653 1.5590952476122018
481.13 481.35862683823984 -0.22862683823984753 -5.164688385271067e-2
485.94 481.4164995749685 4.5235004250315 1.021860350507925
482.49 482.3037528502627 0.18624714973731216 4.2073297187840204e-2
483.77 483.6070229944035 0.1629770055964741 3.6816563372465104e-2
491.77 481.0249164343975 10.7450835656025 2.4273181887690556
483.43 482.2081944229683 1.2218055770317164 0.2760063132279849
481.49 482.6905244198958 -1.2005244198957712 -0.2711988922825122
478.78 480.9741288614041 -2.194128861404124 -0.49565448805243767
492.96 485.8565717694332 7.103428230566806 1.6046669568831393
481.36 483.99243959507345 -2.6324395950734356 -0.5946690382578993
486.68 481.76650494734884 4.913495052651172 1.1099602752189677
484.94 483.069724719673 1.8702752803270073 0.42249584921569994
483.01 481.33834961288795 1.671650387112038 0.3776264153858503
488.17 483.1883946104104 4.9816053895896175 1.1253464244922151
490.41 480.1679106982307 10.24208930176934 2.313691606156222
483.11 482.4149038683481 0.6950961316518942 0.15702246269194528
485.89 480.94068220101354 4.949317798986442 1.1180526463224945
487.08 482.508645049916 4.571354950083958 1.0326707046913566
477.8 480.01746628251317 -2.2174662825131577 -0.5009264197587914
489.96 480.63940670945976 9.320593290540216 2.1055253303633577
486.92 483.0108446487773 3.9091553512226938 0.883079580425271
486.37 482.57972730795177 3.7902726920482337 0.8562239455498787
488.2 483.51586402481416 4.684135975185825 1.0581479782654901
479.06 481.6634377951154 -2.603437795115383 -0.5881175213603873
480.05 484.68450470880435 -4.634504708804343 -1.0469362575856187
487.18 482.8218608903564 4.358139109643616 0.9845051707078616
480.47 481.8880244206695 -1.4180244206694965 -0.32033221960491765
480.36 480.6306788292839 -0.2706788292838951 -6.11464435454739e-2
487.85 479.89671820679695 7.953281793203075 1.7966491781271794
486.11 479.6914116057231 6.418588394276924 1.449961394951398
481.83 481.1970697561745 0.6329302438254558 0.1429791665816065
482.96 482.17217802621536 0.7878219737846166 0.17796926331974147
483.92 481.3074409763495 2.612559023650533 0.590178010121793
477.69 479.64992318380445 -1.9599231838044489 -0.4427473424095181
474.25 480.70714895561014 -6.457148955610137 -1.4586722394340677
479.08 479.7024675196716 -0.6224675196716021 -0.14061563348410486
478.89 481.00544489343537 -2.115444893435381 -0.4778797517789611
483.11 482.38901084355183 0.7209891564481836 0.16287170617772706
488.43 481.25646633043965 7.173533669560356 1.6205038004183012
483.28 480.33371483717946 2.946285162820516 0.6655668633335223
486.76 482.5311759738776 4.228824026122368 0.9552928474721311
476.58 480.67721106043905 -4.097211060439065 -0.9255614318409298
481.61 482.53257783094546 -0.9225778309454427 -0.20841065925050425
477.8 480.0330510466423 -2.233051046642288 -0.5044470235035043
475.32 479.3324132109004 -4.012413210900434 -0.9064055675522111
475.89 478.2499419685471 -2.359941968547105 -0.5331117277702286
485.03 480.3355565472517 4.69444345274826 1.0604764411029242
482.46 479.7315598782737 2.728440121726294 0.6163555912803304
484.57 477.91894784424176 6.6510521557582365 1.502475041125319
483.94 483.45191519870116 0.48808480129883947 0.11025852973791857
482.39 482.34452319301437 4.547680698561862e-2 1.027322682875218e-2
483.8 478.45760011663003 5.342399883369978 1.2068500286116204
482.22 478.7638216096892 3.4561783903108108 0.7807519242835766
481.52 479.1388800137473 2.3811199862526564 0.5378958494817917
483.79 477.1846287648614 6.605371235138648 1.4921557049542535
480.54 476.81117998099177 3.7288200190082534 0.8423417649127792
477.27 480.84424359067077 -3.5742435906707897 -0.8074228949228237
474.5 480.1364995691749 -5.636499569174873 -1.273287251952606
475.52 479.2235127059344 -3.703512705934429 -0.8366248339128552
481.44 478.91505388939413 2.5249461106058675 0.5703862219885535
480.6 476.210862698602 4.389137301398023 0.9915076732202934
487.19 481.0254321330136 6.164567866986374 1.392578067734949
475.42 480.36098930984286 -4.940989309842848 -1.1161712376708273
476.22 478.51210495606927 -2.292104956069238 -0.5177873225895746
485.13 479.57731721621883 5.552682783781165 1.2543530104022107
488.02 484.33140555054337 3.688594449456616 0.8332547944829863
477.78 478.4450809561189 -0.6650809561189135 -0.15024202389261102
477.2 480.5031526805204 -3.303152680520384 -0.7461833621634392
467.56 479.2169410835439 -11.65694108354387 -2.6333071255094267
485.18 477.6146348725092 7.565365127490793 1.7090186657480726
483.52 478.33312476559934 5.186875234400645 1.17171695524459
480.21 479.4778900760471 0.7321099239528621 0.16538389150158914
478.81 481.48536176155926 -2.675361761559259 -0.6043651708916123
484.67 477.9675154808001 6.702484519199913 1.5140936302699408
477.9 479.6817134321857 -1.781713432185711 -0.40248969630754267
475.17 477.5050067316079 -2.335006731607905 -0.5274788489010923
485.73 478.32045063849523 7.409549361504787 1.673819828943716
479.91 478.1399555772117 1.7700444227883168 0.3998536629456538
486.4 479.65037308403333 6.749626915966644 1.5247431144210337
480.15 477.1324329554068 3.017567044593193 0.681669465709775
480.58 482.82343628916425 -2.243436289164265 -0.5067930534728822
484.07 478.16947013024355 5.90052986975644 1.3329317905059794
481.89 480.6437911412516 1.246208858748389 0.2815190232236669
483.14 478.8928744938167 4.247125506183295 0.9594271583094607
479.31 476.1246111330079 3.1853888669921275 0.7195804749163808
484.21 477.288235770853 6.921764229146959 1.563628994525865
476.02 478.30600580479216 -2.2860058047921825 -0.5164095221527084
480.69 478.2957350932866 2.3942649067133743 0.5408652916763936
481.91 476.52270993699136 5.387290063008663 1.2169907361146226
485.06 478.99917896902446 6.060821030975546 1.3691416206809235
485.29 480.8674382556021 4.42256174439791 0.9990582667496749
482.39 481.1210453702997 1.2689546297002607 0.2866573009496584
478.25 478.8354389662744 -0.5854389662744097 -0.1322508701375881
475.79 476.29244393984663 -0.5024439398466143 -0.11350226422907182
485.87 479.0178844308566 6.852115569143393 1.5478953375265612
479.23 476.4582419334783 2.771758066521727 0.6261411303745675
478.61 480.1903466285615 -1.5803466285614718 -0.3570008639436786
479.94 479.4487267515188 0.4912732484812068 0.11097880108736301
479.25 479.3384367489267 -8.84367489267106e-2 -1.997789295120947e-2
480.99 477.44189376811596 3.5481062318840486 0.8015184563019332
481.07 476.33561360755584 4.734386392444151 1.0694995653480546
480.4 482.3769169335795 -1.9769169335795027 -0.44658623651141477
482.8 476.04420182940044 6.755798170599576 1.5261372030315674
480.08 479.65335282852305 0.42664717147692954 9.637974736911713e-2
475.0 478.6696951676176 -3.66969516761759 -0.8289854400119429
483.88 476.696926422392 7.183073577608013 1.6226588690300885
482.52 476.90393713153463 5.616062868465349 1.2686705940133918
478.45 479.2188844607746 -0.7688844607745864 -0.17369127241360752
482.3 475.81261283946816 6.487387160531853 1.465503060651426
472.45 476.2100211409317 -3.7600211409317126 -0.8493901094223798
480.2 480.2141595165933 -1.415951659333814e-2 -3.19863982083975e-3
478.38 474.9481764100585 3.431823589941473 0.775250166241454
472.77 479.30598211413803 -6.535982114138051 -1.476480677907779
483.53 476.3744577455605 7.155542254439467 1.6164395333609067
475.47 478.6980048877349 -3.228004887734869 -0.7292074491181413
467.24 476.41215657483474 -9.17215657483473 -2.0719934236347326
481.03 480.7338755379764 0.29612446202355613 6.689462100697262e-2
482.37 480.51130475015583 1.8586952498441747 0.41987991622217147
484.97 478.0206284049 6.949371595100047 1.5698655082870474
479.53 475.4980717304681 4.031928269531875 0.9108140262190783
482.8 476.4769333498689 6.323066650131125 1.4283829990671366
477.26 480.5658974037096 -3.3058974037095936 -0.7468033961054397
479.02 478.9378167534134 8.218324658656684e-2 1.8565224554443056e-2
476.69 479.483969889582 -2.7939698895820015 -0.631158789082455
476.62 476.72728884411293 -0.10728884411292938 -2.423658794064658e-2
475.69 475.1283411969007 0.5616588030993057 0.1268789228414677
482.95 477.43108128919135 5.518918710808634 1.2467256943415417
483.24 479.0201634085648 4.2198365914351825 0.9532625827884375
484.86 476.63324412261045 8.226755877389564 1.858427070746631
491.97 478.3337308000573 13.636269199942717 3.080438049074982
474.88 478.39283560851754 -3.5128356085175483 -0.7935508099728905
475.64 477.10087603877 -1.4608760387700386 -0.33001241533337206
484.96 478.16396362897893 6.796036371021046 1.5352270267793358
475.42 478.96772021173297 -3.547720211732951 -0.8014312542128782
480.38 475.6006326388746 4.7793673611254235 1.0796607821279804
478.82 474.9766634864767 3.8433365135232975 0.8682110816429235
482.55 478.786077505979 3.763922494021017 0.8502714264690703
480.14 478.9365615888623 1.2034384111377108 0.271857163937664
482.55 476.1723094438278 6.377690556172183 1.4407225588170043
477.91 478.2490255806092 -0.33902558060918864 -7.658599891256687e-2
476.25 474.4577268339357 1.7922731660643194 0.4048751439362759
471.13 478.43777544278043 -7.307775442780439 -1.6508290646045036
482.16 478.00197412694763 4.158025873052395 0.9392995195813987
480.87 479.3152324207446 1.5547675792553832 0.3512225476325008
477.34 477.2801935898294 5.980641017055177e-2 1.3510289270963245e-2
483.66 478.285031656868 5.374968343132025 1.214207255223955
481.95 475.9420528274367 6.007947172563263 1.357197397311141
479.68 476.17198214059135 3.5080178594086533 0.7924624787403274
478.66 474.34503134979343 4.314968650206595 0.9747529486084029
478.8 479.7691576930105 -0.9691576930105157 -0.2189330666129607
481.12 475.82678857769963 5.293211422300374 1.1957383378087658
476.54 478.0366119605891 -1.496611960589064 -0.33808517274788225
478.03 477.46151999839185 0.5684800016081226 0.12841983400410018
479.23 479.110912113517 0.1190878864830438 2.6901995797195863e-2
480.74 477.72481326338215 3.0151867366178635 0.6811317532938489
478.88 479.54303529435083 -0.6630352943508342 -0.14977990817360218
481.05 479.71268358186353 1.3373164181364814 0.3021002532054435
473.54 473.26068816423447 0.2793118357655544 6.309664277182285e-2
469.73 476.05175958076205 -6.321759580762034 -1.4280877316330394
475.51 476.88388448180046 -1.3738844818004736 -0.31036099175789383
476.67 475.61433131158714 1.0556686884128794 0.23847593115995214
472.16 477.7130066863276 -5.553006686327592 -1.2544261801023373
481.85 475.2673812565115 6.582618743488524 1.487015909020143
479.45 479.3846135509556 6.538644904441071e-2 1.4770822031817277e-2
482.38 475.5344685772051 6.84553142279492 1.5464079765310332
469.58 473.85672752722735 -4.276727527227365 -0.9661142653632034
477.93 477.3826135030455 0.5473864969545161 0.12365480382094843
478.21 477.2300569616709 0.9799430383290542 0.2213694799459989
477.62 479.265495182268 -1.6454951822680073 -0.371717945334288
472.46 472.7773808573311 -0.3173808573311021 -7.16964482466269e-2
467.37 473.2887424901299 -5.918742490129887 -1.3370460279083884
473.2 475.32128019247375 -2.121280192473762 -0.4791979479015218
480.05 476.83702080523557 3.2129791947644435 0.7258131397464832
469.65 473.90133694043874 -4.251336940438762 -0.9603785228015735
485.23 477.4312500724956 7.798749927504446 1.761740374853143
477.88 474.53026960482526 3.3497303951747313 0.756705284425051
475.21 475.5632280329792 -0.35322803297924565 -7.97943379405968e-2
475.91 476.45899184845075 -0.5489918484507257 -0.12401745329336308
477.85 475.16451288467897 2.6854871153210524 0.6066524918978817
464.86 472.95056743270436 -8.090567432704347 -1.827662052785967
466.05 473.09691475779204 -7.046914757792024 -1.591900543337891
463.16 472.93274352761154 -9.77274352761151 -2.2076662292962226
475.75 478.4561215361668 -2.7061215361667905 -0.6113138148859982
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439.01 443.764677908941 -4.754677908941005 -1.0740834261221295
453.17 449.2796285666682 3.890371433331836 0.8788362867110385
-- Now we can display the RMSE as a Histogram. Clearly this shows that the RMSE is centered around 0 with the vast majority of the error within 2 RMSEs.
SELECT Within_RSME  from Power_Plant_RMSE_Evaluation
Within_RSME
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We can see this definitively if we count the number of predictions within + or - 1.0 and + or - 2.0 and display this as a pie chart:

SELECT case when Within_RSME <= 1.0 and Within_RSME >= -1.0 then 1  when  Within_RSME <= 2.0 and Within_RSME >= -2.0 then 2 else 3 end RSME_Multiple, COUNT(*) count  from Power_Plant_RMSE_Evaluation
group by case when Within_RSME <= 1.0 and Within_RSME >= -1.0 then 1  when  Within_RSME <= 2.0 and Within_RSME >= -2.0 then 2 else 3 end
RSME_Multiple count
1.0 1267.0
3.0 77.0
2.0 512.0

So we have about 70% of our training data within 1 RMSE and about 97% (70% + 27%) within 2 RMSE. So the model is pretty decent. Let's see if we can tune the model to improve it further.

NOTE: these numbers will vary across runs due to the seed in random sampling of training and test set, number of iterations, and other stopping rules in optimization, for example.

Step 7: Tuning and Evaluation

Now that we have a model with all of the data let's try to make a better model by tuning over several parameters.

import org.apache.spark.ml.tuning.{ParamGridBuilder, CrossValidator}
import org.apache.spark.ml.evaluation._
import org.apache.spark.ml.tuning.{ParamGridBuilder, CrossValidator}
import org.apache.spark.ml.evaluation._

First let's use a cross validator to split the data into training and validation subsets. See http://spark.apache.org/docs/latest/ml-tuning.html.

//Let's set up our evaluator class to judge the model based on the best root mean squared error
val regEval = new RegressionEvaluator()
regEval.setLabelCol("PE")
  .setPredictionCol("Predicted_PE")
  .setMetricName("rmse")
regEval: org.apache.spark.ml.evaluation.RegressionEvaluator = RegressionEvaluator: uid=regEval_c75f9d66a6cb, metricName=rmse, throughOrigin=false
res101: regEval.type = RegressionEvaluator: uid=regEval_c75f9d66a6cb, metricName=rmse, throughOrigin=false

We now treat the lrPipeline as an Estimator, wrapping it in a CrossValidator instance.

This will allow us to jointly choose parameters for all Pipeline stages.

A CrossValidator requires an Estimator, an Evaluator (which we set next).

//Let's create our crossvalidator with 3 fold cross validation
val crossval = new CrossValidator()
crossval.setEstimator(lrPipeline)
crossval.setNumFolds(3)
crossval.setEvaluator(regEval)
crossval: org.apache.spark.ml.tuning.CrossValidator = cv_bc136566b6a6
res102: crossval.type = cv_bc136566b6a6

A CrossValidator also requires a set of EstimatorParamMaps which we set next.

For this we need a regularization parameter (more generally a hyper-parameter that is model-specific).

Now, let's tune over our regularization parameter from 0.01 to 0.10.

val regParam = ((1 to 10) toArray).map(x => (x /100.0))
warning: there was one feature warning; for details, enable `:setting -feature' or `:replay -feature'
regParam: Array[Double] = Array(0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.1)

Check out the scala docs for syntactic details on org.apache.spark.ml.tuning.ParamGridBuilder.

val paramGrid = new ParamGridBuilder()
                    .addGrid(lr.regParam, regParam)
                    .build()
crossval.setEstimatorParamMaps(paramGrid)
paramGrid: Array[org.apache.spark.ml.param.ParamMap] =
Array({
	linReg_3b8dffe4015f-regParam: 0.01
}, {
	linReg_3b8dffe4015f-regParam: 0.02
}, {
	linReg_3b8dffe4015f-regParam: 0.03
}, {
	linReg_3b8dffe4015f-regParam: 0.04
}, {
	linReg_3b8dffe4015f-regParam: 0.05
}, {
	linReg_3b8dffe4015f-regParam: 0.06
}, {
	linReg_3b8dffe4015f-regParam: 0.07
}, {
	linReg_3b8dffe4015f-regParam: 0.08
}, {
	linReg_3b8dffe4015f-regParam: 0.09
}, {
	linReg_3b8dffe4015f-regParam: 0.1
})
res103: crossval.type = cv_bc136566b6a6
//Now let's create our model
val cvModel = crossval.fit(trainingSet)
cvModel: org.apache.spark.ml.tuning.CrossValidatorModel = CrossValidatorModel: uid=cv_bc136566b6a6, bestModel=pipeline_07136143d91d, numFolds=3

In addition to CrossValidator Spark also offers TrainValidationSplit for hyper-parameter tuning. TrainValidationSplit only evaluates each combination of parameters once as opposed to k times in case of CrossValidator. It is therefore less expensive, but will not produce as reliable results when the training dataset is not sufficiently large.

Now that we have tuned let's see what we got for tuning parameters and what our RMSE was versus our intial model

val predictionsAndLabels = cvModel.transform(testSet)
val metrics = new RegressionMetrics(predictionsAndLabels.select("Predicted_PE", "PE").rdd.map(r => (r(0).asInstanceOf[Double], r(1).asInstanceOf[Double])))

val rmse = metrics.rootMeanSquaredError
val explainedVariance = metrics.explainedVariance
val r2 = metrics.r2
predictionsAndLabels: org.apache.spark.sql.DataFrame = [AT: double, V: double ... 5 more fields]
metrics: org.apache.spark.mllib.evaluation.RegressionMetrics = org.apache.spark.mllib.evaluation.RegressionMetrics@671c9416
rmse: Double = 4.4286032895695895
explainedVariance: Double = 271.5750243564875
r2: Double = 0.9313732865178349
println (f"Root Mean Squared Error: $rmse")
println (f"Explained Variance: $explainedVariance")  
println (f"R2: $r2")
Root Mean Squared Error: 4.4286032895695895
Explained Variance: 271.5750243564875
R2: 0.9313732865178349

So our initial untuned and tuned linear regression models are statistically identical.

Given that the only linearly correlated variable is Temperature, it makes sense try another machine learning method such a Decision Tree to handle non-linear data and see if we can improve our model

A Decision Tree creates a model based on splitting variables using a tree structure. We will first start with a single decision tree model.

Reference Decision Trees: https://en.wikipedia.org/wiki/Decisiontreelearning

//Let's build a decision tree pipeline
import org.apache.spark.ml.regression.DecisionTreeRegressor

// we are using a Decision Tree Regressor as opposed to a classifier we used for the hand-written digit classification problem
val dt = new DecisionTreeRegressor()
dt.setLabelCol("PE")
dt.setPredictionCol("Predicted_PE")
dt.setFeaturesCol("features")
dt.setMaxBins(100)

val dtPipeline = new Pipeline()
dtPipeline.setStages(Array(vectorizer, dt))
import org.apache.spark.ml.regression.DecisionTreeRegressor
dt: org.apache.spark.ml.regression.DecisionTreeRegressor = dtr_92691f930484
dtPipeline: org.apache.spark.ml.Pipeline = pipeline_ddfeb1cfff04
res106: dtPipeline.type = pipeline_ddfeb1cfff04
//Let's just resuse our CrossValidator
crossval.setEstimator(dtPipeline)
res107: crossval.type = cv_bc136566b6a6
val paramGrid = new ParamGridBuilder()
                     .addGrid(dt.maxDepth, Array(2, 3))
                     .build()
paramGrid: Array[org.apache.spark.ml.param.ParamMap] =
Array({
	dtr_92691f930484-maxDepth: 2
}, {
	dtr_92691f930484-maxDepth: 3
})
crossval.setEstimatorParamMaps(paramGrid)
res108: crossval.type = cv_bc136566b6a6
val dtModel = crossval.fit(trainingSet) // fit decitionTree with cv
dtModel: org.apache.spark.ml.tuning.CrossValidatorModel = CrossValidatorModel: uid=cv_bc136566b6a6, bestModel=pipeline_ddfeb1cfff04, numFolds=3
import org.apache.spark.ml.regression.DecisionTreeRegressionModel
import org.apache.spark.ml.PipelineModel
dtModel.bestModel.asInstanceOf[PipelineModel].stages.last.asInstanceOf[DecisionTreeRegressionModel].toDebugString
import org.apache.spark.ml.regression.DecisionTreeRegressionModel
import org.apache.spark.ml.PipelineModel
res109: String =
"DecisionTreeRegressionModel: uid=dtr_92691f930484, depth=3, numNodes=15, numFeatures=4
  If (feature 0 <= 18.595)
   If (feature 0 <= 11.885000000000002)
    If (feature 0 <= 8.575)
     Predict: 483.994943457189
    Else (feature 0 > 8.575)
     Predict: 476.04374262101527
   Else (feature 0 > 11.885000000000002)
    If (feature 0 <= 15.475000000000001)
     Predict: 467.5564649956784
    Else (feature 0 > 15.475000000000001)
     Predict: 459.5010376134889
  Else (feature 0 > 18.595)
   If (feature 1 <= 66.21000000000001)
    If (feature 0 <= 22.055)
     Predict: 452.01076923076914
    Else (feature 0 > 22.055)
     Predict: 443.46937926330156
   Else (feature 1 > 66.21000000000001)
    If (feature 0 <= 25.325)
     Predict: 440.73731707317074
    Else (feature 0 > 25.325)
     Predict: 433.86131215469624
"

The line above will pull the Decision Tree model from the Pipeline and display it as an if-then-else string.

Next let's visualize it as a decision tree for regression.

display(dtModel.bestModel.asInstanceOf[PipelineModel].stages.last.asInstanceOf[DecisionTreeRegressionModel])
treeNode
{"index":7,"featureType":"continuous","prediction":null,"threshold":18.595,"categories":null,"feature":0,"overflow":false}
{"index":3,"featureType":"continuous","prediction":null,"threshold":11.885000000000002,"categories":null,"feature":0,"overflow":false}
{"index":1,"featureType":"continuous","prediction":null,"threshold":8.575,"categories":null,"feature":0,"overflow":false}
{"index":0,"featureType":null,"prediction":483.994943457189,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":2,"featureType":null,"prediction":476.04374262101527,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":5,"featureType":"continuous","prediction":null,"threshold":15.475000000000001,"categories":null,"feature":0,"overflow":false}
{"index":4,"featureType":null,"prediction":467.5564649956784,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":6,"featureType":null,"prediction":459.5010376134889,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":11,"featureType":"continuous","prediction":null,"threshold":66.21000000000001,"categories":null,"feature":1,"overflow":false}
{"index":9,"featureType":"continuous","prediction":null,"threshold":22.055,"categories":null,"feature":0,"overflow":false}
{"index":8,"featureType":null,"prediction":452.01076923076914,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":10,"featureType":null,"prediction":443.46937926330156,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":13,"featureType":"continuous","prediction":null,"threshold":25.325,"categories":null,"feature":0,"overflow":false}
{"index":12,"featureType":null,"prediction":440.73731707317074,"threshold":null,"categories":null,"feature":null,"overflow":false}
{"index":14,"featureType":null,"prediction":433.86131215469624,"threshold":null,"categories":null,"feature":null,"overflow":false}

Now let's see how our DecisionTree model compares to our LinearRegression model

val predictionsAndLabels = dtModel.bestModel.transform(testSet)
val metrics = new RegressionMetrics(predictionsAndLabels.select("Predicted_PE", "PE").map(r => (r(0).asInstanceOf[Double], r(1).asInstanceOf[Double])).rdd)

val rmse = metrics.rootMeanSquaredError
val explainedVariance = metrics.explainedVariance
val r2 = metrics.r2

println (f"Root Mean Squared Error: $rmse")
println (f"Explained Variance: $explainedVariance")  
println (f"R2: $r2")
Root Mean Squared Error: 5.111944542729953
Explained Variance: 261.4355220034205
R2: 0.908560906504635
predictionsAndLabels: org.apache.spark.sql.DataFrame = [AT: double, V: double ... 5 more fields]
metrics: org.apache.spark.mllib.evaluation.RegressionMetrics = org.apache.spark.mllib.evaluation.RegressionMetrics@684c4c50
rmse: Double = 5.111944542729953
explainedVariance: Double = 261.4355220034205
r2: Double = 0.908560906504635

So our DecisionTree was slightly worse than our LinearRegression model (LR: 4.6 vs DT: 5.2). Maybe we can try an Ensemble method such as Gradient-Boosted Decision Trees to see if we can strengthen our model by using an ensemble of weaker trees with weighting to reduce the error in our model.

*Note since this is a complex model, the cell below can take about *16 minutes* or so to run on a small cluster with a couple nodes with about 6GB RAM, go out and grab a coffee and come back :-).*

This GBTRegressor code will be way faster on a larger cluster of course.

A visual explanation of gradient boosted trees:

Let's see what a boosting algorithm, a type of ensemble method, is all about in more detail.

import org.apache.spark.ml.regression.GBTRegressor

val gbt = new GBTRegressor()
gbt.setLabelCol("PE")
gbt.setPredictionCol("Predicted_PE")
gbt.setFeaturesCol("features")
gbt.setSeed(100088121L)
gbt.setMaxBins(100)
gbt.setMaxIter(120)

val gbtPipeline = new Pipeline()
gbtPipeline.setStages(Array(vectorizer, gbt))
//Let's just resuse our CrossValidator

crossval.setEstimator(gbtPipeline)

val paramGrid = new ParamGridBuilder()
  .addGrid(gbt.maxDepth, Array(2, 3))
  .build()
crossval.setEstimatorParamMaps(paramGrid)

//gbt.explainParams
val gbtModel = crossval.fit(trainingSet)
import org.apache.spark.ml.regression.GBTRegressor
gbt: org.apache.spark.ml.regression.GBTRegressor = gbtr_0a275b363831
gbtPipeline: org.apache.spark.ml.Pipeline = pipeline_8b2722444cff
paramGrid: Array[org.apache.spark.ml.param.ParamMap] =
Array({
	gbtr_0a275b363831-maxDepth: 2
}, {
	gbtr_0a275b363831-maxDepth: 3
})
gbtModel: org.apache.spark.ml.tuning.CrossValidatorModel = CrossValidatorModel: uid=cv_bc136566b6a6, bestModel=pipeline_8b2722444cff, numFolds=3
import org.apache.spark.ml.regression.GBTRegressionModel 

val predictionsAndLabels = gbtModel.bestModel.transform(testSet)
val metrics = new RegressionMetrics(predictionsAndLabels.select("Predicted_PE", "PE").map(r => (r(0).asInstanceOf[Double], r(1).asInstanceOf[Double])).rdd)

val rmse = metrics.rootMeanSquaredError
val explainedVariance = metrics.explainedVariance
val r2 = metrics.r2


println (f"Root Mean Squared Error: $rmse")
println (f"Explained Variance: $explainedVariance")  
println (f"R2: $r2")
Root Mean Squared Error: 3.7034735091301307
Explained Variance: 272.208177448154
R2: 0.9520069744321176
import org.apache.spark.ml.regression.GBTRegressionModel
predictionsAndLabels: org.apache.spark.sql.DataFrame = [AT: double, V: double ... 5 more fields]
metrics: org.apache.spark.mllib.evaluation.RegressionMetrics = org.apache.spark.mllib.evaluation.RegressionMetrics@79d7946a
rmse: Double = 3.7034735091301307
explainedVariance: Double = 272.208177448154
r2: Double = 0.9520069744321176

We can use the toDebugString method to dump out what our trees and weighting look like:

gbtModel.bestModel.asInstanceOf[PipelineModel].stages.last.asInstanceOf[GBTRegressionModel].toDebugString
res116: String =
"GBTRegressionModel: uid=gbtr_0a275b363831, numTrees=120, numFeatures=4
  Tree 0 (weight 1.0):
    If (feature 0 <= 18.595)
     If (feature 0 <= 11.885000000000002)
      If (feature 0 <= 8.575)
       Predict: 483.994943457189
      Else (feature 0 > 8.575)
       Predict: 476.04374262101527
     Else (feature 0 > 11.885000000000002)
      If (feature 0 <= 15.475000000000001)
       Predict: 467.5564649956784
      Else (feature 0 > 15.475000000000001)
       Predict: 459.5010376134889
    Else (feature 0 > 18.595)
     If (feature 1 <= 66.21000000000001)
      If (feature 0 <= 22.055)
       Predict: 452.01076923076914
      Else (feature 0 > 22.055)
       Predict: 443.46937926330156
     Else (feature 1 > 66.21000000000001)
      If (feature 0 <= 25.325)
       Predict: 440.73731707317074
      Else (feature 0 > 25.325)
       Predict: 433.86131215469624
  Tree 1 (weight 0.1):
    If (feature 3 <= 82.55000000000001)
     If (feature 0 <= 26.505000000000003)
      If (feature 3 <= 64.11500000000001)
       Predict: 6.095232469256877
      Else (feature 3 > 64.11500000000001)
       Predict: 1.4337156041793564
     Else (feature 0 > 26.505000000000003)
      If (feature 1 <= 65.55000000000001)
       Predict: -7.6527692217902885
      Else (feature 1 > 65.55000000000001)
       Predict: -0.5844786594493007
    Else (feature 3 > 82.55000000000001)
     If (feature 1 <= 45.754999999999995)
      If (feature 3 <= 93.075)
       Predict: 0.6108402960070604
      Else (feature 3 > 93.075)
       Predict: -3.913147108789527
     Else (feature 1 > 45.754999999999995)
      If (feature 0 <= 18.595)
       Predict: -9.443118256805649
      Else (feature 0 > 18.595)
       Predict: -3.9650066253122347
  Tree 2 (weight 0.1):
    If (feature 1 <= 45.754999999999995)
     If (feature 0 <= 15.475000000000001)
      If (feature 0 <= 14.285)
       Predict: 1.1090321642566017
      Else (feature 0 > 14.285)
       Predict: -3.898383406004269
     Else (feature 0 > 15.475000000000001)
      If (feature 0 <= 18.595)
       Predict: 4.874047316205584
      Else (feature 0 > 18.595)
       Predict: 10.653531335032094
    Else (feature 1 > 45.754999999999995)
     If (feature 0 <= 18.595)
      If (feature 1 <= 58.19)
       Predict: -5.0005796708960615
      Else (feature 1 > 58.19)
       Predict: -13.749053154552547
     Else (feature 0 > 18.595)
      If (feature 2 <= 1009.295)
       Predict: -3.1410617295379555
      Else (feature 2 > 1009.295)
       Predict: 0.8001319329379373
  Tree 3 (weight 0.1):
    If (feature 3 <= 85.52000000000001)
     If (feature 1 <= 55.825)
      If (feature 0 <= 26.505000000000003)
       Predict: 2.695149105254423
      Else (feature 0 > 26.505000000000003)
       Predict: -6.7564705067621675
     Else (feature 1 > 55.825)
      If (feature 1 <= 66.21000000000001)
       Predict: -2.282355645191304
      Else (feature 1 > 66.21000000000001)
       Predict: 0.5508297910243797
    Else (feature 3 > 85.52000000000001)
     If (feature 1 <= 40.629999999999995)
      If (feature 2 <= 1022.8399999999999)
       Predict: 2.236331037122985
      Else (feature 2 > 1022.8399999999999)
       Predict: -7.220151471077029
     Else (feature 1 > 40.629999999999995)
      If (feature 3 <= 89.595)
       Predict: -2.175085332960937
      Else (feature 3 > 89.595)
       Predict: -4.54715329410012
  Tree 4 (weight 0.1):
    If (feature 2 <= 1010.335)
     If (feature 1 <= 43.005)
      If (feature 0 <= 15.475000000000001)
       Predict: -0.004818717215773318
      Else (feature 0 > 15.475000000000001)
       Predict: 5.355639866401019
     Else (feature 1 > 43.005)
      If (feature 1 <= 65.15)
       Predict: -5.132340755716604
      Else (feature 1 > 65.15)
       Predict: -0.7228608840382099
    Else (feature 2 > 1010.335)
     If (feature 3 <= 74.525)
      If (feature 0 <= 29.455)
       Predict: 3.0313483965828176
      Else (feature 0 > 29.455)
       Predict: -2.560863167947768
     Else (feature 3 > 74.525)
      If (feature 1 <= 40.629999999999995)
       Predict: 2.228142113797423
      Else (feature 1 > 40.629999999999995)
       Predict: -1.6052323952407273
  Tree 5 (weight 0.1):
    If (feature 3 <= 81.045)
     If (feature 0 <= 27.585)
      If (feature 3 <= 46.92)
       Predict: 8.005444802948366
      Else (feature 3 > 46.92)
       Predict: 1.301219291279602
     Else (feature 0 > 27.585)
      If (feature 1 <= 65.55000000000001)
       Predict: -6.568175152421089
      Else (feature 1 > 65.55000000000001)
       Predict: -0.8331220915230161
    Else (feature 3 > 81.045)
     If (feature 1 <= 41.519999999999996)
      If (feature 2 <= 1019.835)
       Predict: 1.7054425589091675
      Else (feature 2 > 1019.835)
       Predict: -2.6266728146418195
     Else (feature 1 > 41.519999999999996)
      If (feature 1 <= 41.805)
       Predict: -11.130585327952137
      Else (feature 1 > 41.805)
       Predict: -2.111742422947989
  Tree 6 (weight 0.1):
    If (feature 2 <= 1009.625)
     If (feature 1 <= 43.005)
      If (feature 0 <= 15.475000000000001)
       Predict: -0.4497329015715072
      Else (feature 0 > 15.475000000000001)
       Predict: 3.661440765591046
     Else (feature 1 > 43.005)
      If (feature 1 <= 66.85499999999999)
       Predict: -3.861085082339984
      Else (feature 1 > 66.85499999999999)
       Predict: -0.7492674320362704
    Else (feature 2 > 1009.625)
     If (feature 3 <= 69.32499999999999)
      If (feature 0 <= 29.455)
       Predict: 2.621042446270476
      Else (feature 0 > 29.455)
       Predict: -1.4554021183385886
     Else (feature 3 > 69.32499999999999)
      If (feature 1 <= 58.19)
       Predict: 0.42605173456002876
      Else (feature 1 > 58.19)
       Predict: -1.9554878629891888
  Tree 7 (weight 0.1):
    If (feature 3 <= 86.625)
     If (feature 1 <= 52.795)
      If (feature 0 <= 18.595)
       Predict: 0.4988124937300424
      Else (feature 0 > 18.595)
       Predict: 4.447321094438702
     Else (feature 1 > 52.795)
      If (feature 1 <= 66.21000000000001)
       Predict: -1.721618872277871
      Else (feature 1 > 66.21000000000001)
       Predict: 0.6365209437219329
    Else (feature 3 > 86.625)
     If (feature 0 <= 6.895)
      If (feature 3 <= 87.32499999999999)
       Predict: -10.224737687790185
      Else (feature 3 > 87.32499999999999)
       Predict: 3.712660431036073
     Else (feature 0 > 6.895)
      If (feature 0 <= 8.575)
       Predict: -7.105091794629204
      Else (feature 0 > 8.575)
       Predict: -1.5060749360589718
  Tree 8 (weight 0.1):
    If (feature 2 <= 1008.745)
     If (feature 1 <= 41.665)
      If (feature 0 <= 15.475000000000001)
       Predict: 0.11492519898093705
      Else (feature 0 > 15.475000000000001)
       Predict: 3.532699993937119
     Else (feature 1 > 41.665)
      If (feature 1 <= 66.85499999999999)
       Predict: -3.366654434213031
      Else (feature 1 > 66.85499999999999)
       Predict: -0.9165259817521934
    Else (feature 2 > 1008.745)
     If (feature 3 <= 82.955)
      If (feature 1 <= 51.905)
       Predict: 1.841638760642105
      Else (feature 1 > 51.905)
       Predict: 0.33265178659776373
     Else (feature 3 > 82.955)
      If (feature 3 <= 95.68)
       Predict: -0.4850135884105616
      Else (feature 3 > 95.68)
       Predict: -3.812639024859598
  Tree 9 (weight 0.1):
    If (feature 0 <= 29.455)
     If (feature 3 <= 61.89)
      If (feature 1 <= 71.18)
       Predict: 1.9301726185107941
      Else (feature 1 > 71.18)
       Predict: 8.938327477606107
     Else (feature 3 > 61.89)
      If (feature 0 <= 5.8149999999999995)
       Predict: 4.428862111265314
      Else (feature 0 > 5.8149999999999995)
       Predict: -0.3308347482908286
    Else (feature 0 > 29.455)
     If (feature 1 <= 68.28999999999999)
      If (feature 2 <= 1009.875)
       Predict: -8.941194411728706
      Else (feature 2 > 1009.875)
       Predict: -1.8834474815204216
     Else (feature 1 > 68.28999999999999)
      If (feature 2 <= 1014.405)
       Predict: -0.5760094442636617
      Else (feature 2 > 1014.405)
       Predict: -5.50575933697771
  Tree 10 (weight 0.1):
    If (feature 2 <= 1005.345)
     If (feature 0 <= 27.355)
      If (feature 3 <= 99.3)
       Predict: -0.5544332197918127
      Else (feature 3 > 99.3)
       Predict: -6.049841121821514
     Else (feature 0 > 27.355)
      If (feature 1 <= 70.815)
       Predict: -8.03479585317622
      Else (feature 1 > 70.815)
       Predict: 0.0619269945107018
    Else (feature 2 > 1005.345)
     If (feature 3 <= 72.41499999999999)
      If (feature 0 <= 24.755000000000003)
       Predict: 2.020104454165069
      Else (feature 0 > 24.755000000000003)
       Predict: -0.22964512858748945
     Else (feature 3 > 72.41499999999999)
      If (feature 1 <= 40.7)
       Predict: 1.2987210163143512
      Else (feature 1 > 40.7)
       Predict: -0.8347660227231797
  Tree 11 (weight 0.1):
    If (feature 0 <= 5.0600000000000005)
     If (feature 1 <= 42.3)
      If (feature 1 <= 39.765)
       Predict: 4.261094449524424
      Else (feature 1 > 39.765)
       Predict: 9.140536590115639
     Else (feature 1 > 42.3)
      If (feature 2 <= 1007.835)
       Predict: 0.9746298984436711
      Else (feature 2 > 1007.835)
       Predict: -6.317973546286112
    Else (feature 0 > 5.0600000000000005)
     If (feature 3 <= 95.68)
      If (feature 2 <= 1009.295)
       Predict: -0.8626626541525325
      Else (feature 2 > 1009.295)
       Predict: 0.3906915507169364
     Else (feature 3 > 95.68)
      If (feature 0 <= 11.885000000000002)
       Predict: -6.002679638413293
      Else (feature 0 > 11.885000000000002)
       Predict: -0.7509189525586508
  Tree 12 (weight 0.1):
    If (feature 0 <= 18.595)
     If (feature 1 <= 51.905)
      If (feature 0 <= 13.695)
       Predict: 0.5958576966099496
      Else (feature 0 > 13.695)
       Predict: -1.2694566117501789
     Else (feature 1 > 51.905)
      If (feature 1 <= 58.19)
       Predict: -4.248373100253223
      Else (feature 1 > 58.19)
       Predict: -9.144729000689791
    Else (feature 0 > 18.595)
     If (feature 1 <= 47.64)
      If (feature 2 <= 1012.675)
       Predict: 0.8560563666774771
      Else (feature 2 > 1012.675)
       Predict: 10.801233083620462
     Else (feature 1 > 47.64)
      If (feature 0 <= 20.015)
       Predict: 3.1978561830060213
      Else (feature 0 > 20.015)
       Predict: -0.16716555702980626
  Tree 13 (weight 0.1):
    If (feature 0 <= 28.655)
     If (feature 1 <= 66.21000000000001)
      If (feature 1 <= 58.19)
       Predict: 0.34765099851241454
      Else (feature 1 > 58.19)
       Predict: -1.8189329025195076
     Else (feature 1 > 66.21000000000001)
      If (feature 0 <= 22.525)
       Predict: 6.490484815153365
      Else (feature 0 > 22.525)
       Predict: 0.7933381751314565
    Else (feature 0 > 28.655)
     If (feature 1 <= 68.28999999999999)
      If (feature 2 <= 1005.665)
       Predict: -8.922459399148678
      Else (feature 2 > 1005.665)
       Predict: -2.3989441108132668
     Else (feature 1 > 68.28999999999999)
      If (feature 2 <= 1018.215)
       Predict: -0.3023338438804105
      Else (feature 2 > 1018.215)
       Predict: 14.559949112833806
  Tree 14 (weight 0.1):
    If (feature 0 <= 15.475000000000001)
     If (feature 0 <= 13.695)
      If (feature 0 <= 11.885000000000002)
       Predict: -0.8897676968273979
      Else (feature 0 > 11.885000000000002)
       Predict: 3.5874467728768487
     Else (feature 0 > 13.695)
      If (feature 1 <= 46.345)
       Predict: -3.2690852418064273
      Else (feature 1 > 46.345)
       Predict: -8.844433418899179
    Else (feature 0 > 15.475000000000001)
     If (feature 1 <= 43.175)
      If (feature 1 <= 41.805)
       Predict: 3.298855216614116
      Else (feature 1 > 41.805)
       Predict: 9.150659154207167
     Else (feature 1 > 43.175)
      If (feature 2 <= 1012.495)
       Predict: -0.7109832273625656
      Else (feature 2 > 1012.495)
       Predict: 1.1631179843236674
  Tree 15 (weight 0.1):
    If (feature 3 <= 90.055)
     If (feature 0 <= 30.41)
      If (feature 1 <= 66.21000000000001)
       Predict: -0.01732155577258642
      Else (feature 1 > 66.21000000000001)
       Predict: 1.3432966941310502
     Else (feature 0 > 30.41)
      If (feature 1 <= 69.465)
       Predict: -3.6657811330207344
      Else (feature 1 > 69.465)
       Predict: -0.38803561342243853
    Else (feature 3 > 90.055)
     If (feature 2 <= 1015.725)
      If (feature 1 <= 47.64)
       Predict: 1.5063080039677825
      Else (feature 1 > 47.64)
       Predict: -1.860635777865782
     Else (feature 2 > 1015.725)
      If (feature 1 <= 40.7)
       Predict: 0.21921885078759318
      Else (feature 1 > 40.7)
       Predict: -4.793242614118129
  Tree 16 (weight 0.1):
    If (feature 0 <= 6.895)
     If (feature 3 <= 67.42500000000001)
      If (feature 1 <= 39.620000000000005)
       Predict: -1.8477082180199003
      Else (feature 1 > 39.620000000000005)
       Predict: 16.387935166882745
     Else (feature 3 > 67.42500000000001)
      If (feature 0 <= 5.0600000000000005)
       Predict: 4.152127693563297
      Else (feature 0 > 5.0600000000000005)
       Predict: 0.7556214745509566
    Else (feature 0 > 6.895)
     If (feature 0 <= 8.575)
      If (feature 2 <= 1022.8399999999999)
       Predict: -2.9436476590152036
      Else (feature 2 > 1022.8399999999999)
       Predict: -8.032234733606465
     Else (feature 0 > 8.575)
      If (feature 0 <= 9.325)
       Predict: 5.082738415532321
      Else (feature 0 > 9.325)
       Predict: -0.032287806549855816
  Tree 17 (weight 0.1):
    If (feature 3 <= 61.89)
     If (feature 0 <= 28.655)
      If (feature 0 <= 11.885000000000002)
       Predict: -4.455566502931916
      Else (feature 0 > 11.885000000000002)
       Predict: 1.9027943448616742
     Else (feature 0 > 28.655)
      If (feature 1 <= 66.21000000000001)
       Predict: -3.1810487244675034
      Else (feature 1 > 66.21000000000001)
       Predict: 0.11525363261816625
    Else (feature 3 > 61.89)
     If (feature 1 <= 43.175)
      If (feature 0 <= 18.595)
       Predict: 0.22262511130066664
      Else (feature 0 > 18.595)
       Predict: 10.13639446335034
     Else (feature 1 > 43.175)
      If (feature 0 <= 22.055)
       Predict: -1.4775024201129299
      Else (feature 0 > 22.055)
       Predict: 0.20591189539330298
  Tree 18 (weight 0.1):
    If (feature 2 <= 1005.345)
     If (feature 1 <= 70.815)
      If (feature 0 <= 23.564999999999998)
       Predict: -0.178777362918765
      Else (feature 0 > 23.564999999999998)
       Predict: -4.52113806132068
     Else (feature 1 > 70.815)
      If (feature 3 <= 60.025000000000006)
       Predict: 4.247605743793766
      Else (feature 3 > 60.025000000000006)
       Predict: -0.26865379510738685
    Else (feature 2 > 1005.345)
     If (feature 1 <= 66.21000000000001)
      If (feature 1 <= 55.825)
       Predict: 0.3773109266288433
      Else (feature 1 > 55.825)
       Predict: -1.3659380946007862
     Else (feature 1 > 66.21000000000001)
      If (feature 0 <= 21.335)
       Predict: 8.448170645066464
      Else (feature 0 > 21.335)
       Predict: 0.5048679905700459
  Tree 19 (weight 0.1):
    If (feature 0 <= 18.595)
     If (feature 1 <= 51.905)
      If (feature 0 <= 17.655)
       Predict: -0.003054757854134698
      Else (feature 0 > 17.655)
       Predict: -2.9290357116654935
     Else (feature 1 > 51.905)
      If (feature 1 <= 66.525)
       Predict: -4.061825439604536
      Else (feature 1 > 66.525)
       Predict: -11.67844591879286
    Else (feature 0 > 18.595)
     If (feature 0 <= 23.945)
      If (feature 3 <= 74.525)
       Predict: 3.807909998319029
      Else (feature 3 > 74.525)
       Predict: 0.008459259251505081
     Else (feature 0 > 23.945)
      If (feature 1 <= 74.915)
       Predict: -0.6429811796826012
      Else (feature 1 > 74.915)
       Predict: 2.099670946504916
  Tree 20 (weight 0.1):
    If (feature 0 <= 15.475000000000001)
     If (feature 0 <= 14.285)
      If (feature 0 <= 11.885000000000002)
       Predict: -0.7234702732306101
      Else (feature 0 > 11.885000000000002)
       Predict: 1.589299673192479
     Else (feature 0 > 14.285)
      If (feature 2 <= 1016.495)
       Predict: -2.4381805412578545
      Else (feature 2 > 1016.495)
       Predict: -6.544687605774689
    Else (feature 0 > 15.475000000000001)
     If (feature 1 <= 43.005)
      If (feature 2 <= 1008.405)
       Predict: 0.8119248626873221
      Else (feature 2 > 1008.405)
       Predict: 5.506769369239865
     Else (feature 1 > 43.005)
      If (feature 2 <= 1012.935)
       Predict: -0.5028175384892806
      Else (feature 2 > 1012.935)
       Predict: 1.0290531238165197
  Tree 21 (weight 0.1):
    If (feature 0 <= 6.895)
     If (feature 3 <= 67.42500000000001)
      If (feature 1 <= 39.620000000000005)
       Predict: -0.9752219334588972
      Else (feature 1 > 39.620000000000005)
       Predict: 13.369575512848845
     Else (feature 3 > 67.42500000000001)
      If (feature 1 <= 42.705)
       Predict: 1.850492181024754
      Else (feature 1 > 42.705)
       Predict: -2.033710059657357
    Else (feature 0 > 6.895)
     If (feature 0 <= 8.575)
      If (feature 2 <= 1022.8399999999999)
       Predict: -2.256120115332435
      Else (feature 2 > 1022.8399999999999)
       Predict: -6.380948299395909
     Else (feature 0 > 8.575)
      If (feature 0 <= 9.594999999999999)
       Predict: 3.4448565562285904
      Else (feature 0 > 9.594999999999999)
       Predict: -0.05858832726578875
  Tree 22 (weight 0.1):
    If (feature 0 <= 22.055)
     If (feature 0 <= 21.095)
      If (feature 1 <= 66.21000000000001)
       Predict: -0.17987193554240402
      Else (feature 1 > 66.21000000000001)
       Predict: 6.044335675519052
     Else (feature 0 > 21.095)
      If (feature 1 <= 66.21000000000001)
       Predict: -5.809637597188877
      Else (feature 1 > 66.21000000000001)
       Predict: 2.7761443044302214
    Else (feature 0 > 22.055)
     If (feature 0 <= 23.564999999999998)
      If (feature 1 <= 64.74000000000001)
       Predict: 5.951769778696803
      Else (feature 1 > 64.74000000000001)
       Predict: -0.30197045172071896
     Else (feature 0 > 23.564999999999998)
      If (feature 1 <= 44.519999999999996)
       Predict: -7.283292958317056
      Else (feature 1 > 44.519999999999996)
       Predict: -0.19387573131258415
  Tree 23 (weight 0.1):
    If (feature 3 <= 53.025000000000006)
     If (feature 0 <= 24.945)
      If (feature 0 <= 18.29)
       Predict: 1.0381040338364682
      Else (feature 0 > 18.29)
       Predict: 5.164469183375362
     Else (feature 0 > 24.945)
      If (feature 1 <= 66.21000000000001)
       Predict: -1.0707595335847206
      Else (feature 1 > 66.21000000000001)
       Predict: 0.8108674466901084
    Else (feature 3 > 53.025000000000006)
     If (feature 1 <= 73.725)
      If (feature 1 <= 71.505)
       Predict: -0.0525992725981239
      Else (feature 1 > 71.505)
       Predict: -2.807221561152817
     Else (feature 1 > 73.725)
      If (feature 2 <= 1017.295)
       Predict: 1.037788102485777
      Else (feature 2 > 1017.295)
       Predict: 7.287181806639116
  Tree 24 (weight 0.1):
    If (feature 2 <= 1004.505)
     If (feature 1 <= 70.815)
      If (feature 1 <= 59.144999999999996)
       Predict: -0.3743851611431973
      Else (feature 1 > 59.144999999999996)
       Predict: -4.648812647772385
     Else (feature 1 > 70.815)
      If (feature 0 <= 27.884999999999998)
       Predict: 2.4545579195950995
      Else (feature 0 > 27.884999999999998)
       Predict: -0.32777974793969294
    Else (feature 2 > 1004.505)
     If (feature 0 <= 22.055)
      If (feature 0 <= 20.795)
       Predict: 0.045218490740101897
      Else (feature 0 > 20.795)
       Predict: -3.3620385127109333
     Else (feature 0 > 22.055)
      If (feature 0 <= 22.955)
       Predict: 4.485324626081587
      Else (feature 0 > 22.955)
       Predict: 0.13166549369330485
  Tree 25 (weight 0.1):
    If (feature 0 <= 18.595)
     If (feature 1 <= 58.19)
      If (feature 0 <= 17.655)
       Predict: -0.023636417468335308
      Else (feature 0 > 17.655)
       Predict: -2.607492744918568
     Else (feature 1 > 58.19)
      If (feature 1 <= 66.525)
       Predict: -4.8994505786627665
      Else (feature 1 > 66.525)
       Predict: -10.07085237281708
    Else (feature 0 > 18.595)
     If (feature 0 <= 19.725)
      If (feature 1 <= 66.21000000000001)
       Predict: 2.2716539497960406
      Else (feature 1 > 66.21000000000001)
       Predict: 13.879740983230867
     Else (feature 0 > 19.725)
      If (feature 1 <= 43.005)
       Predict: 5.616411926544602
      Else (feature 1 > 43.005)
       Predict: -0.00532316539213451
  Tree 26 (weight 0.1):
    If (feature 3 <= 93.075)
     If (feature 1 <= 55.825)
      If (feature 0 <= 22.055)
       Predict: 0.15441544139943786
      Else (feature 0 > 22.055)
       Predict: 2.7626508552722306
     Else (feature 1 > 55.825)
      If (feature 1 <= 66.21000000000001)
       Predict: -1.2060290652635515
      Else (feature 1 > 66.21000000000001)
       Predict: 0.4827535356971057
    Else (feature 3 > 93.075)
     If (feature 2 <= 1015.725)
      If (feature 0 <= 7.34)
       Predict: 4.241421869391143
      Else (feature 0 > 7.34)
       Predict: -0.704916847045625
     Else (feature 2 > 1015.725)
      If (feature 0 <= 11.885000000000002)
       Predict: -5.4904249010577795
      Else (feature 0 > 11.885000000000002)
       Predict: 0.0976872424106726
  Tree 27 (weight 0.1):
    If (feature 2 <= 1008.745)
     If (feature 1 <= 41.665)
      If (feature 1 <= 39.765)
       Predict: -1.0511879426704696
      Else (feature 1 > 39.765)
       Predict: 1.894883627758776
     Else (feature 1 > 41.665)
      If (feature 1 <= 41.805)
       Predict: -13.576686832482961
      Else (feature 1 > 41.805)
       Predict: -0.7168167899342832
    Else (feature 2 > 1008.745)
     If (feature 0 <= 15.475000000000001)
      If (feature 0 <= 13.695)
       Predict: 0.303140697564446
      Else (feature 0 > 13.695)
       Predict: -2.8034862119109945
     Else (feature 0 > 15.475000000000001)
      If (feature 1 <= 55.825)
       Predict: 2.0736158373993576
      Else (feature 1 > 55.825)
       Predict: -0.03336709818500243
  Tree 28 (weight 0.1):
    If (feature 2 <= 1001.785)
     If (feature 3 <= 69.86500000000001)
      If (feature 1 <= 69.465)
       Predict: -7.299995136853619
      Else (feature 1 > 69.465)
       Predict: 0.23757420536270835
     Else (feature 3 > 69.86500000000001)
      If (feature 0 <= 7.34)
       Predict: 3.4313360513286284
      Else (feature 0 > 7.34)
       Predict: -1.276734468456009
    Else (feature 2 > 1001.785)
     If (feature 0 <= 11.885000000000002)
      If (feature 0 <= 11.335)
       Predict: 0.04499264982858887
      Else (feature 0 > 11.335)
       Predict: -6.156735713959919
     Else (feature 0 > 11.885000000000002)
      If (feature 0 <= 12.715)
       Predict: 4.4864210547378915
      Else (feature 0 > 12.715)
       Predict: 0.030721690290287165
  Tree 29 (weight 0.1):
    If (feature 1 <= 66.21000000000001)
     If (feature 0 <= 26.505000000000003)
      If (feature 0 <= 22.055)
       Predict: -0.3694472776628706
      Else (feature 0 > 22.055)
       Predict: 1.5208925945902059
     Else (feature 0 > 26.505000000000003)
      If (feature 1 <= 43.510000000000005)
       Predict: -17.99975152056241
      Else (feature 1 > 43.510000000000005)
       Predict: -2.4033598663496183
    Else (feature 1 > 66.21000000000001)
     If (feature 0 <= 22.055)
      If (feature 0 <= 18.595)
       Predict: -7.600012529438
      Else (feature 0 > 18.595)
       Predict: 6.469471961408998
     Else (feature 0 > 22.055)
      If (feature 0 <= 25.325)
       Predict: -2.6540186758683166
      Else (feature 0 > 25.325)
       Predict: 0.9869775581610103
  Tree 30 (weight 0.1):
    If (feature 0 <= 5.0600000000000005)
     If (feature 1 <= 42.3)
      If (feature 3 <= 95.68)
       Predict: 2.6307256050737506
      Else (feature 3 > 95.68)
       Predict: 7.168878406232186
     Else (feature 1 > 42.3)
      If (feature 2 <= 1007.835)
       Predict: -0.1884983669158752
      Else (feature 2 > 1007.835)
       Predict: -5.920088632100639
    Else (feature 0 > 5.0600000000000005)
     If (feature 1 <= 37.815)
      If (feature 0 <= 11.885000000000002)
       Predict: -3.8096010917307517
      Else (feature 0 > 11.885000000000002)
       Predict: 3.5943708074284917
     Else (feature 1 > 37.815)
      If (feature 1 <= 41.519999999999996)
       Predict: 0.6752927073561888
      Else (feature 1 > 41.519999999999996)
       Predict: -0.14342050966250913
  Tree 31 (weight 0.1):
    If (feature 3 <= 99.3)
     If (feature 0 <= 31.155)
      If (feature 3 <= 46.92)
       Predict: 2.011051499336945
      Else (feature 3 > 46.92)
       Predict: 0.012791339921714258
     Else (feature 0 > 31.155)
      If (feature 2 <= 1014.405)
       Predict: -0.916397796921109
      Else (feature 2 > 1014.405)
       Predict: -6.832504867736499
    Else (feature 3 > 99.3)
     If (feature 1 <= 39.765)
      If (feature 1 <= 38.41)
       Predict: -5.505405887296888
      Else (feature 1 > 38.41)
       Predict: -16.748187635942333
     Else (feature 1 > 39.765)
      If (feature 0 <= 16.04)
       Predict: 0.7708563952983728
      Else (feature 0 > 16.04)
       Predict: -3.909609799859729
  Tree 32 (weight 0.1):
    If (feature 1 <= 66.21000000000001)
     If (feature 1 <= 64.74000000000001)
      If (feature 2 <= 1011.515)
       Predict: -1.0002623040885374
      Else (feature 2 > 1011.515)
       Predict: 0.3591184679910596
     Else (feature 1 > 64.74000000000001)
      If (feature 2 <= 1006.775)
       Predict: -13.788703659238209
      Else (feature 2 > 1006.775)
       Predict: -2.4620285364725656
    Else (feature 1 > 66.21000000000001)
     If (feature 1 <= 69.09)
      If (feature 0 <= 22.525)
       Predict: 6.088217885246919
      Else (feature 0 > 22.525)
       Predict: 1.0364537580784474
     Else (feature 1 > 69.09)
      If (feature 0 <= 25.325)
       Predict: -2.7946704533493856
      Else (feature 0 > 25.325)
       Predict: 0.6607665941219878
  Tree 33 (weight 0.1):
    If (feature 2 <= 1028.14)
     If (feature 0 <= 29.455)
      If (feature 1 <= 66.21000000000001)
       Predict: -0.08158010506593574
      Else (feature 1 > 66.21000000000001)
       Predict: 0.8815313937000332
     Else (feature 0 > 29.455)
      If (feature 1 <= 44.519999999999996)
       Predict: -12.581939252812768
      Else (feature 1 > 44.519999999999996)
       Predict: -0.77008278158028
    Else (feature 2 > 1028.14)
     If (feature 0 <= 8.575)
      If (feature 1 <= 39.45)
       Predict: 0.6766771966451415
      Else (feature 1 > 39.45)
       Predict: -8.445008186341592
     Else (feature 0 > 8.575)
      If (feature 0 <= 8.96)
       Predict: 3.777292703648982
      Else (feature 0 > 8.96)
       Predict: -2.398045803854934
  Tree 34 (weight 0.1):
    If (feature 0 <= 6.895)
     If (feature 3 <= 67.42500000000001)
      If (feature 1 <= 39.620000000000005)
       Predict: -0.6804590872791323
      Else (feature 1 > 39.620000000000005)
       Predict: 10.518093452986212
     Else (feature 3 > 67.42500000000001)
      If (feature 1 <= 42.705)
       Predict: 1.3098801739379287
      Else (feature 1 > 42.705)
       Predict: -1.7450883352732074
    Else (feature 0 > 6.895)
     If (feature 0 <= 8.575)
      If (feature 0 <= 7.765)
       Predict: -0.7816329288490581
      Else (feature 0 > 7.765)
       Predict: -3.7319393815256547
     Else (feature 0 > 8.575)
      If (feature 0 <= 9.965)
       Predict: 2.5600814387681337
      Else (feature 0 > 9.965)
       Predict: -0.06944896856946733
  Tree 35 (weight 0.1):
    If (feature 3 <= 61.89)
     If (feature 1 <= 39.34)
      If (feature 0 <= 16.695)
       Predict: -4.078381955056753
      Else (feature 0 > 16.695)
       Predict: -16.616821684050763
     Else (feature 1 > 39.34)
      If (feature 1 <= 40.82)
       Predict: 4.4394084324272045
      Else (feature 1 > 40.82)
       Predict: 0.4663514281701948
    Else (feature 3 > 61.89)
     If (feature 1 <= 58.19)
      If (feature 0 <= 22.055)
       Predict: -0.027831559557693095
      Else (feature 0 > 22.055)
       Predict: 2.492136574233702
     Else (feature 1 > 58.19)
      If (feature 0 <= 18.595)
       Predict: -4.183073089901298
      Else (feature 0 > 18.595)
       Predict: -0.40866909936948326
  Tree 36 (weight 0.1):
    If (feature 2 <= 1004.505)
     If (feature 1 <= 38.754999999999995)
      If (feature 3 <= 77.195)
       Predict: 9.579430817769946
      Else (feature 3 > 77.195)
       Predict: 2.6305173165509195
     Else (feature 1 > 38.754999999999995)
      If (feature 1 <= 70.065)
       Predict: -1.801035005150415
      Else (feature 1 > 70.065)
       Predict: 0.4054557218074593
    Else (feature 2 > 1004.505)
     If (feature 2 <= 1017.475)
      If (feature 1 <= 43.175)
       Predict: 1.09341093192285
      Else (feature 1 > 43.175)
       Predict: -0.03229585395374685
     Else (feature 2 > 1017.475)
      If (feature 2 <= 1019.365)
       Predict: -1.7719467091167656
      Else (feature 2 > 1019.365)
       Predict: 0.2537098831339789
  Tree 37 (weight 0.1):
    If (feature 0 <= 15.475000000000001)
     If (feature 0 <= 13.695)
      If (feature 0 <= 11.885000000000002)
       Predict: -0.5104239863875834
      Else (feature 0 > 11.885000000000002)
       Predict: 2.1202163252308432
     Else (feature 0 > 13.695)
      If (feature 3 <= 78.38499999999999)
       Predict: -3.379040627299855
      Else (feature 3 > 78.38499999999999)
       Predict: -0.9911440360990582
    Else (feature 0 > 15.475000000000001)
     If (feature 0 <= 16.395)
      If (feature 3 <= 67.42500000000001)
       Predict: 0.4887402058080506
      Else (feature 3 > 67.42500000000001)
       Predict: 3.884289185845989
     Else (feature 0 > 16.395)
      If (feature 2 <= 1020.565)
       Predict: -0.02862374251288089
      Else (feature 2 > 1020.565)
       Predict: 3.15734851002617
  Tree 38 (weight 0.1):
    If (feature 3 <= 43.385)
     If (feature 0 <= 24.945)
      If (feature 2 <= 1014.405)
       Predict: 1.603183026814036
      Else (feature 2 > 1014.405)
       Predict: 7.05673098720603
     Else (feature 0 > 24.945)
      If (feature 0 <= 26.295)
       Predict: -5.886157652325024
      Else (feature 0 > 26.295)
       Predict: 0.7387886738447553
    Else (feature 3 > 43.385)
     If (feature 1 <= 73.725)
      If (feature 1 <= 71.505)
       Predict: 0.008754170391068655
      Else (feature 1 > 71.505)
       Predict: -2.0178119354056765
     Else (feature 1 > 73.725)
      If (feature 1 <= 77.42)
       Predict: 1.8396223170900134
      Else (feature 1 > 77.42)
       Predict: -1.5747478023010713
  Tree 39 (weight 0.1):
    If (feature 0 <= 22.055)
     If (feature 0 <= 20.795)
      If (feature 0 <= 18.595)
       Predict: -0.25201916420658693
      Else (feature 0 > 18.595)
       Predict: 1.5718496558845116
     Else (feature 0 > 20.795)
      If (feature 1 <= 66.21000000000001)
       Predict: -3.7201562729508804
      Else (feature 1 > 66.21000000000001)
       Predict: 2.087916157719636
    Else (feature 0 > 22.055)
     If (feature 0 <= 23.564999999999998)
      If (feature 2 <= 1012.015)
       Predict: 0.7371264627237751
      Else (feature 2 > 1012.015)
       Predict: 4.6381746481309065
     Else (feature 0 > 23.564999999999998)
      If (feature 1 <= 44.519999999999996)
       Predict: -5.772062593218147
      Else (feature 1 > 44.519999999999996)
       Predict: -0.12977023255758624
  Tree 40 (weight 0.1):
    If (feature 0 <= 5.0600000000000005)
     If (feature 3 <= 95.68)
      If (feature 2 <= 1011.105)
       Predict: -3.365769010003795
      Else (feature 2 > 1011.105)
       Predict: 2.955050770650336
     Else (feature 3 > 95.68)
      If (feature 2 <= 1008.205)
       Predict: 2.728200788704399
      Else (feature 2 > 1008.205)
       Predict: 6.919382935391042
    Else (feature 0 > 5.0600000000000005)
     If (feature 3 <= 96.61)
      If (feature 1 <= 37.815)
       Predict: -1.3949762323292278
      Else (feature 1 > 37.815)
       Predict: 0.06411431759031856
     Else (feature 3 > 96.61)
      If (feature 0 <= 11.605)
       Predict: -3.491961189446582
      Else (feature 0 > 11.605)
       Predict: -0.16406940197018208
  Tree 41 (weight 0.1):
    If (feature 0 <= 30.41)
     If (feature 1 <= 66.21000000000001)
      If (feature 1 <= 58.85)
       Predict: 0.15540001609212736
      Else (feature 1 > 58.85)
       Predict: -1.1352706510871309
     Else (feature 1 > 66.21000000000001)
      If (feature 0 <= 25.325)
       Predict: -0.6390388689881783
      Else (feature 0 > 25.325)
       Predict: 1.3909471658872326
    Else (feature 0 > 30.41)
     If (feature 2 <= 1014.405)
      If (feature 1 <= 56.894999999999996)
       Predict: -9.841212730443857
      Else (feature 1 > 56.894999999999996)
       Predict: -0.5054201979116707
     Else (feature 2 > 1014.405)
      If (feature 1 <= 74.915)
       Predict: -5.898616989217175
      Else (feature 1 > 74.915)
       Predict: 1.042314191558674
  Tree 42 (weight 0.1):
    If (feature 2 <= 1009.625)
     If (feature 1 <= 43.005)
      If (feature 1 <= 42.025000000000006)
       Predict: -0.05077288158998095
      Else (feature 1 > 42.025000000000006)
       Predict: 3.619244461816007
     Else (feature 1 > 43.005)
      If (feature 0 <= 18.595)
       Predict: -3.5057172058309307
      Else (feature 0 > 18.595)
       Predict: -0.32537979322253646
    Else (feature 2 > 1009.625)
     If (feature 2 <= 1017.475)
      If (feature 1 <= 55.825)
       Predict: 0.8076710222538108
      Else (feature 1 > 55.825)
       Predict: -0.01784249647067053
     Else (feature 2 > 1017.475)
      If (feature 2 <= 1019.365)
       Predict: -1.4312272708033218
      Else (feature 2 > 1019.365)
       Predict: 0.20844195286029432
  Tree 43 (weight 0.1):
    If (feature 0 <= 18.595)
     If (feature 0 <= 17.655)
      If (feature 0 <= 15.475000000000001)
       Predict: -0.2913115404147692
      Else (feature 0 > 15.475000000000001)
       Predict: 1.1145997107947745
     Else (feature 0 > 17.655)
      If (feature 1 <= 37.815)
       Predict: 14.538914074443028
      Else (feature 1 > 37.815)
       Predict: -3.0407663665320683
    Else (feature 0 > 18.595)
     If (feature 2 <= 1020.325)
      If (feature 1 <= 43.175)
       Predict: 3.881117973012625
      Else (feature 1 > 43.175)
       Predict: 0.04538590552170286
     Else (feature 2 > 1020.325)
      If (feature 1 <= 64.74000000000001)
       Predict: 4.662857871344832
      Else (feature 1 > 64.74000000000001)
       Predict: -43.5190245896606
  Tree 44 (weight 0.1):
    If (feature 0 <= 6.895)
     If (feature 3 <= 67.42500000000001)
      If (feature 1 <= 39.620000000000005)
       Predict: -0.7153417257252007
      Else (feature 1 > 39.620000000000005)
       Predict: 8.417772324738223
     Else (feature 3 > 67.42500000000001)
      If (feature 2 <= 1010.985)
       Predict: 2.5111312207852263
      Else (feature 2 > 1010.985)
       Predict: 0.29950092637128345
    Else (feature 0 > 6.895)
     If (feature 0 <= 8.575)
      If (feature 1 <= 40.06)
       Predict: -3.30672576579827
      Else (feature 1 > 40.06)
       Predict: -0.45097750406116727
     Else (feature 0 > 8.575)
      If (feature 0 <= 9.325)
       Predict: 3.226884779601992
      Else (feature 0 > 9.325)
       Predict: -0.041218673012550146
  Tree 45 (weight 0.1):
    If (feature 2 <= 1028.14)
     If (feature 0 <= 10.395)
      If (feature 3 <= 92.22999999999999)
       Predict: 1.0355113706204075
      Else (feature 3 > 92.22999999999999)
       Predict: -1.4603765116034264
     Else (feature 0 > 10.395)
      If (feature 0 <= 11.885000000000002)
       Predict: -2.630098257038007
      Else (feature 0 > 11.885000000000002)
       Predict: 0.09582680902226459
    Else (feature 2 > 1028.14)
     If (feature 0 <= 8.575)
      If (feature 1 <= 39.45)
       Predict: 1.107359449029309
      Else (feature 1 > 39.45)
       Predict: -6.096185488604492
     Else (feature 0 > 8.575)
      If (feature 3 <= 70.57499999999999)
       Predict: -3.516006231223605
      Else (feature 3 > 70.57499999999999)
       Predict: -0.26144006873351155
  Tree 46 (weight 0.1):
    If (feature 0 <= 27.884999999999998)
     If (feature 1 <= 66.21000000000001)
      If (feature 0 <= 25.145)
       Predict: 0.06412914679730906
      Else (feature 0 > 25.145)
       Predict: -1.554041618425865
     Else (feature 1 > 66.21000000000001)
      If (feature 0 <= 25.325)
       Predict: -0.4748636523867588
      Else (feature 0 > 25.325)
       Predict: 2.4595627925276826
    Else (feature 0 > 27.884999999999998)
     If (feature 3 <= 61.89)
      If (feature 1 <= 71.895)
       Predict: -0.4429995884239883
      Else (feature 1 > 71.895)
       Predict: 1.4321627506429122
     Else (feature 3 > 61.89)
      If (feature 1 <= 71.505)
       Predict: -0.2617373838209719
      Else (feature 1 > 71.505)
       Predict: -2.637373068367584
  Tree 47 (weight 0.1):
    If (feature 3 <= 61.89)
     If (feature 1 <= 39.34)
      If (feature 0 <= 16.695)
       Predict: -2.855821258258964
      Else (feature 0 > 16.695)
       Predict: -13.80709248590955
     Else (feature 1 > 39.34)
      If (feature 1 <= 74.915)
       Predict: 0.35443616318343385
      Else (feature 1 > 74.915)
       Predict: 2.9400682899293233
    Else (feature 3 > 61.89)
     If (feature 1 <= 71.505)
      If (feature 1 <= 66.85499999999999)
       Predict: -0.142107366817925
      Else (feature 1 > 66.85499999999999)
       Predict: 1.0352328327059535
     Else (feature 1 > 71.505)
      If (feature 1 <= 73.00999999999999)
       Predict: -2.947898208728739
      Else (feature 1 > 73.00999999999999)
       Predict: -0.0830706492691125
  Tree 48 (weight 0.1):
    If (feature 2 <= 1004.505)
     If (feature 1 <= 38.754999999999995)
      If (feature 3 <= 86.625)
       Predict: 4.921331281961159
      Else (feature 3 > 86.625)
       Predict: -5.961237317667383
     Else (feature 1 > 38.754999999999995)
      If (feature 1 <= 39.765)
       Predict: -4.436072018762161
      Else (feature 1 > 39.765)
       Predict: -0.7283906418193187
    Else (feature 2 > 1004.505)
     If (feature 0 <= 22.055)
      If (feature 0 <= 20.795)
       Predict: 0.044899959208437666
      Else (feature 0 > 20.795)
       Predict: -2.2295677836603995
     Else (feature 0 > 22.055)
      If (feature 0 <= 23.564999999999998)
       Predict: 2.3559950404053414
      Else (feature 0 > 23.564999999999998)
       Predict: -0.06950420285239005
  Tree 49 (weight 0.1):
    If (feature 1 <= 41.435)
     If (feature 0 <= 11.885000000000002)
      If (feature 0 <= 11.335)
       Predict: -0.02697483446966382
      Else (feature 0 > 11.335)
       Predict: -3.7031660865730367
     Else (feature 0 > 11.885000000000002)
      If (feature 0 <= 13.265)
       Predict: 4.209724879257512
      Else (feature 0 > 13.265)
       Predict: 0.41602586770224464
    Else (feature 1 > 41.435)
     If (feature 1 <= 41.805)
      If (feature 3 <= 89.595)
       Predict: -1.6099299736449546
      Else (feature 3 > 89.595)
       Predict: -9.419799062932288
     Else (feature 1 > 41.805)
      If (feature 1 <= 43.175)
       Predict: 1.5951066240527068
      Else (feature 1 > 43.175)
       Predict: -0.11481901338423915
  Tree 50 (weight 0.1):
    If (feature 1 <= 38.41)
     If (feature 0 <= 11.885000000000002)
      If (feature 2 <= 1016.665)
       Predict: -5.344526613859499
      Else (feature 2 > 1016.665)
       Predict: 0.058134490545794976
     Else (feature 0 > 11.885000000000002)
      If (feature 0 <= 16.985)
       Predict: 1.537246393097642
      Else (feature 0 > 16.985)
       Predict: 9.920778277565365
    Else (feature 1 > 38.41)
     If (feature 0 <= 13.485)
      If (feature 1 <= 51.045)
       Predict: 0.6675749827847329
      Else (feature 1 > 51.045)
       Predict: -5.737026170963195
     Else (feature 0 > 13.485)
      If (feature 0 <= 15.475000000000001)
       Predict: -1.7210713764803844
      Else (feature 0 > 15.475000000000001)
       Predict: 0.09027853735147576
  Tree 51 (weight 0.1):
    If (feature 0 <= 31.155)
     If (feature 3 <= 48.230000000000004)
      If (feature 2 <= 1020.325)
       Predict: 0.9307527734280435
      Else (feature 2 > 1020.325)
       Predict: 9.070547343579028
     Else (feature 3 > 48.230000000000004)
      If (feature 1 <= 73.725)
       Predict: -0.06359121142988887
      Else (feature 1 > 73.725)
       Predict: 1.049949579330099
    Else (feature 0 > 31.155)
     If (feature 1 <= 63.08)
      If (feature 1 <= 44.519999999999996)
       Predict: -6.355864033256125
      Else (feature 1 > 44.519999999999996)
       Predict: 13.6760008529786
     Else (feature 1 > 63.08)
      If (feature 1 <= 68.28999999999999)
       Predict: -3.953494984806905
      Else (feature 1 > 68.28999999999999)
       Predict: -0.6145841300086397
  Tree 52 (weight 0.1):
    If (feature 2 <= 1012.495)
     If (feature 1 <= 41.435)
      If (feature 1 <= 39.975)
       Predict: -0.4047468839922722
      Else (feature 1 > 39.975)
       Predict: 2.509624688414308
     Else (feature 1 > 41.435)
      If (feature 1 <= 41.805)
       Predict: -6.811044477667833
      Else (feature 1 > 41.805)
       Predict: -0.26889174065489546
    Else (feature 2 > 1012.495)
     If (feature 3 <= 92.22999999999999)
      If (feature 1 <= 58.19)
       Predict: 0.7048711166950787
      Else (feature 1 > 58.19)
       Predict: -0.5475390646726656
     Else (feature 3 > 92.22999999999999)
      If (feature 1 <= 41.805)
       Predict: -3.7013459723577355
      Else (feature 1 > 41.805)
       Predict: 0.7237930378019226
  Tree 53 (weight 0.1):
    If (feature 0 <= 18.595)
     If (feature 0 <= 17.335)
      If (feature 3 <= 74.08500000000001)
       Predict: -0.8631764946312587
      Else (feature 3 > 74.08500000000001)
       Predict: 0.2803856631344212
     Else (feature 0 > 17.335)
      If (feature 1 <= 42.705)
       Predict: 0.9335711174385192
      Else (feature 1 > 42.705)
       Predict: -2.950020164379197
    Else (feature 0 > 18.595)
     If (feature 2 <= 1013.395)
      If (feature 1 <= 66.85499999999999)
       Predict: -0.7231135633124072
      Else (feature 1 > 66.85499999999999)
       Predict: 0.41724670068145925
     Else (feature 2 > 1013.395)
      If (feature 1 <= 58.19)
       Predict: 4.568024116358373
      Else (feature 1 > 58.19)
       Predict: -0.36270787813043714
  Tree 54 (weight 0.1):
    If (feature 2 <= 1001.785)
     If (feature 3 <= 63.575)
      If (feature 3 <= 60.025000000000006)
       Predict: -1.7427137986580719
      Else (feature 3 > 60.025000000000006)
       Predict: -7.776342039375448
     Else (feature 3 > 63.575)
      If (feature 0 <= 27.119999999999997)
       Predict: 0.026174663094801796
      Else (feature 0 > 27.119999999999997)
       Predict: -2.343138620856655
    Else (feature 2 > 1001.785)
     If (feature 0 <= 22.055)
      If (feature 1 <= 66.21000000000001)
       Predict: -0.27236570115397085
      Else (feature 1 > 66.21000000000001)
       Predict: 3.164590339421908
     Else (feature 0 > 22.055)
      If (feature 0 <= 22.725)
       Predict: 2.9597120242025485
      Else (feature 0 > 22.725)
       Predict: 0.054881549113388446
  Tree 55 (weight 0.1):
    If (feature 2 <= 1028.14)
     If (feature 1 <= 45.754999999999995)
      If (feature 0 <= 26.715)
       Predict: 0.2599176823406179
      Else (feature 0 > 26.715)
       Predict: -5.549910372715466
     Else (feature 1 > 45.754999999999995)
      If (feature 0 <= 15.475000000000001)
       Predict: -2.867925531108855
      Else (feature 0 > 15.475000000000001)
       Predict: -0.0236838100703647
    Else (feature 2 > 1028.14)
     If (feature 0 <= 8.575)
      If (feature 1 <= 39.45)
       Predict: 0.7777761733424086
      Else (feature 1 > 39.45)
       Predict: -5.202001886405932
     Else (feature 0 > 8.575)
      If (feature 3 <= 68.945)
       Predict: -3.641368616696809
      Else (feature 3 > 68.945)
       Predict: -0.6008141057791702
  Tree 56 (weight 0.1):
    If (feature 3 <= 61.89)
     If (feature 0 <= 18.29)
      If (feature 2 <= 1019.025)
       Predict: -2.1632736300070996
      Else (feature 2 > 1019.025)
       Predict: 1.2430029950309498
     Else (feature 0 > 18.29)
      If (feature 1 <= 44.91)
       Predict: 3.2134324628571003
      Else (feature 1 > 44.91)
       Predict: 0.2988556025240279
    Else (feature 3 > 61.89)
     If (feature 1 <= 71.505)
      If (feature 1 <= 66.85499999999999)
       Predict: -0.09866504525517336
      Else (feature 1 > 66.85499999999999)
       Predict: 0.7271499788275563
     Else (feature 1 > 71.505)
      If (feature 1 <= 73.00999999999999)
       Predict: -2.395971400707892
      Else (feature 1 > 73.00999999999999)
       Predict: -0.16608323426526406
  Tree 57 (weight 0.1):
    If (feature 2 <= 1017.645)
     If (feature 2 <= 1014.615)
      If (feature 1 <= 43.175)
       Predict: 1.0389282601473917
      Else (feature 1 > 43.175)
       Predict: -0.3646675630154698
     Else (feature 2 > 1014.615)
      If (feature 1 <= 43.510000000000005)
       Predict: -0.6889797697082773
      Else (feature 1 > 43.510000000000005)
       Predict: 1.5908362409321974
    Else (feature 2 > 1017.645)
     If (feature 2 <= 1019.025)
      If (feature 1 <= 71.18)
       Predict: -1.6569133708803008
      Else (feature 1 > 71.18)
       Predict: 4.314967971455512
     Else (feature 2 > 1019.025)
      If (feature 3 <= 89.595)
       Predict: 0.43765066032139976
      Else (feature 3 > 89.595)
       Predict: -1.7344432288008194
  Tree 58 (weight 0.1):
    If (feature 2 <= 1004.505)
     If (feature 1 <= 70.815)
      If (feature 1 <= 59.834999999999994)
       Predict: -0.170418541124326
      Else (feature 1 > 59.834999999999994)
       Predict: -2.895038840312831
     Else (feature 1 > 70.815)
      If (feature 2 <= 1000.505)
       Predict: -1.3832637115340176
      Else (feature 2 > 1000.505)
       Predict: 1.2249185299155396
    Else (feature 2 > 1004.505)
     If (feature 0 <= 22.055)
      If (feature 1 <= 66.21000000000001)
       Predict: -0.2418541439735617
      Else (feature 1 > 66.21000000000001)
       Predict: 3.0110894160107886
     Else (feature 0 > 22.055)
      If (feature 0 <= 23.945)
       Predict: 1.4999960684883906
      Else (feature 0 > 23.945)
       Predict: -0.042407486119460915
  Tree 59 (weight 0.1):
    If (feature 1 <= 77.42)
     If (feature 1 <= 74.915)
      If (feature 1 <= 71.505)
       Predict: 0.03983464447255206
      Else (feature 1 > 71.505)
       Predict: -0.7683021525819648
     Else (feature 1 > 74.915)
      If (feature 3 <= 72.82)
       Predict: 2.774179202497669
      Else (feature 3 > 72.82)
       Predict: -0.32979787820368633
    Else (feature 1 > 77.42)
     If (feature 0 <= 21.595)
      If (feature 0 <= 21.335)
       Predict: -13.565760771414489
      Else (feature 0 > 21.335)
       Predict: -13.954507897669714
     Else (feature 0 > 21.595)
      If (feature 0 <= 22.955)
       Predict: 10.853700477067264
      Else (feature 0 > 22.955)
       Predict: -1.4643467280880287
  Tree 60 (weight 0.1):
    If (feature 0 <= 10.395)
     If (feature 1 <= 40.629999999999995)
      If (feature 3 <= 75.545)
       Predict: -2.3127871072788375
      Else (feature 3 > 75.545)
       Predict: 0.3992391857664209
     Else (feature 1 > 40.629999999999995)
      If (feature 3 <= 89.595)
       Predict: 2.9152362525803523
      Else (feature 3 > 89.595)
       Predict: -1.4086879927580456
    Else (feature 0 > 10.395)
     If (feature 0 <= 11.885000000000002)
      If (feature 2 <= 1025.2150000000001)
       Predict: -2.2352340341897547
      Else (feature 2 > 1025.2150000000001)
       Predict: 5.952010328542228
     Else (feature 0 > 11.885000000000002)
      If (feature 0 <= 12.415)
       Predict: 3.4957190546300447
      Else (feature 0 > 12.415)
       Predict: -0.03992973893781255
  Tree 61 (weight 0.1):
    If (feature 1 <= 40.82)
     If (feature 1 <= 40.224999999999994)
      If (feature 3 <= 75.545)
       Predict: -1.2944988036912455
      Else (feature 3 > 75.545)
       Predict: 0.44866615475817667
     Else (feature 1 > 40.224999999999994)
      If (feature 2 <= 1025.2150000000001)
       Predict: 0.7826360308981203
      Else (feature 2 > 1025.2150000000001)
       Predict: 9.875672812487991
    Else (feature 1 > 40.82)
     If (feature 2 <= 1025.2150000000001)
      If (feature 0 <= 10.945)
       Predict: 1.1628421208118285
      Else (feature 0 > 10.945)
       Predict: -0.12551627485602937
     Else (feature 2 > 1025.2150000000001)
      If (feature 1 <= 41.15)
       Predict: -7.782369290305258
      Else (feature 1 > 41.15)
       Predict: -1.200273276366743
  Tree 62 (weight 0.1):
    If (feature 0 <= 22.055)
     If (feature 0 <= 21.335)
      If (feature 1 <= 66.21000000000001)
       Predict: -0.09621281022933233
      Else (feature 1 > 66.21000000000001)
       Predict: 2.680549669942832
     Else (feature 0 > 21.335)
      If (feature 1 <= 63.864999999999995)
       Predict: -3.207766197974041
      Else (feature 1 > 63.864999999999995)
       Predict: -0.14162445042909583
    Else (feature 0 > 22.055)
     If (feature 0 <= 22.725)
      If (feature 2 <= 1011.515)
       Predict: 0.5064350504779975
      Else (feature 2 > 1011.515)
       Predict: 3.659612527058891
     Else (feature 0 > 22.725)
      If (feature 3 <= 75.545)
       Predict: 0.2595183211083464
      Else (feature 3 > 75.545)
       Predict: -0.6564588168227348
  Tree 63 (weight 0.1):
    If (feature 2 <= 1017.645)
     If (feature 1 <= 44.67)
      If (feature 1 <= 44.13)
       Predict: 0.3869693354075677
      Else (feature 1 > 44.13)
       Predict: 4.723132901950317
     Else (f...

Conclusion

Wow! So our best model is in fact our Gradient Boosted Decision tree model which uses an ensemble of 120 Trees with a depth of 3 to construct a better model than the single decision tree.

Step 8: Deployment will be done later

Now that we have a predictive model it is time to deploy the model into an operational environment.

In our example, let's say we have a series of sensors attached to the power plant and a monitoring station.

The monitoring station will need close to real-time information about how much power that their station will generate so they can relay that to the utility.

For this we need to create a Spark Streaming utility that we can use for this purpose. For this you need to be introduced to basic concepts in Spark Streaming first. See http://spark.apache.org/docs/latest/streaming-programming-guide.html if you can't wait!

After deployment you will be able to use the best predictions from gradient boosed regression trees to feed a real-time dashboard or feed the utility with information on how much power the peaker plant will deliver give current conditions.

Persisting Statistical Machine Learning Models

See https://databricks.com/blog/2016/05/31/apache-spark-2-0-preview-machine-learning-model-persistence.html

Let's save our best model so we can load it without having to rerun the validation and training again.

gbtModel
res117: org.apache.spark.ml.tuning.CrossValidatorModel = CrossValidatorModel: uid=cv_bc136566b6a6, bestModel=pipeline_8b2722444cff, numFolds=3
gbtModel.bestModel.asInstanceOf[PipelineModel]
        .write.overwrite().save("dbfs:///databricks/driver/MyTrainedBestPipelineModel")

When it is time to deploy the trained model to serve predicitons, we can simply reload this model and proceed as shown later.

This is one of the Deploymnet Patterns for Serving a Model's Prediction.

See: https://learning.oreilly.com/library/view/spark-the-definitive/9781491912201/ch24.html#deployment-patterns

Datasource References:

  • Pinar Tüfekci, Prediction of full load electrical power output of a base load operated combined cycle power plant using machine learning methods, International Journal of Electrical Power & Energy Systems, Volume 60, September 2014, Pages 126-140, ISSN 0142-0615, Web Link
  • Heysem Kaya, Pinar Tüfekci , Sadik Fikret Gürgen: Local and Global Learning Methods for Predicting Power of a Combined Gas & Steam Turbine, Proceedings of the International Conference on Emerging Trends in Computer and Electronics Engineering ICETCEE 2012, pp. 13-18 (Mar. 2012, Dubai) Web Link

ScaDaMaLe Course site and book

Activity Recognition from Accelerometer

  1. ETL Using SparkSQL Windows

  1. Prediction using Random Forest

This work is a simpler databricksification of Amira Lakhal's more complex framework for activity recognition:

Amira's video

See Section below on 0. Download and Load Data first.

  • Once data is loaded come back here (if you have not downloaded and loaded data into the distributed file system under your hood).
val data = sc.textFile("dbfs:///datasets/sds/ActivityRecognition/dataTraining.csv") // assumes data is loaded
data: org.apache.spark.rdd.RDD[String] = dbfs:///datasets/sds/ActivityRecognition/dataTraining.csv MapPartitionsRDD[1] at textFile at command-561044440962565:1
data.take(5).foreach(println)
"user_id","activity","timeStampAsLong","x","y","z"
"user_001","Jumping",1446047227606,"4.33079","-12.72175","-3.18118"
"user_001","Jumping",1446047227671,"0.575403","-0.727487","2.95007"
"user_001","Jumping",1446047227735,"-1.60885","3.52607","-0.1922"
"user_001","Jumping",1446047227799,"0.690364","-0.037722","1.72382"
val dataDF = sqlContext.read    
    .format("com.databricks.spark.csv") // use spark.csv package
    .option("header", "true") // Use first line of all files as header
    .option("inferSchema", "true") // Automatically infer data types
    .option("delimiter", ",") // Specify the delimiter as ','
    .load("dbfs:///datasets/sds/ActivityRecognition/dataTraining.csv")
dataDF: org.apache.spark.sql.DataFrame = [user_id: string, activity: string ... 4 more fields]
val dataDFnew = spark.read.format("csv") 
  .option("inferSchema", "true") 
  .option("header", "true") 
  .option("sep", ",") 
  .load("dbfs:///datasets/sds/ActivityRecognition/dataTraining.csv")
dataDFnew: org.apache.spark.sql.DataFrame = [user_id: string, activity: string ... 4 more fields]
dataDFnew.printSchema()
root
 |-- user_id: string (nullable = true)
 |-- activity: string (nullable = true)
 |-- timeStampAsLong: long (nullable = true)
 |-- x: double (nullable = true)
 |-- y: double (nullable = true)
 |-- z: double (nullable = true)
display(dataDF) // zp.show(dataDF)
user_id activity timeStampAsLong x y z
user_001 Jumping 1.446047227606e12 4.33079 -12.72175 -3.18118
user_001 Jumping 1.446047227671e12 0.575403 -0.727487 2.95007
user_001 Jumping 1.446047227735e12 -1.60885 3.52607 -0.1922
user_001 Jumping 1.446047227799e12 0.690364 -3.7722e-2 1.72382
user_001 Jumping 1.446047227865e12 3.44943 -1.68549 2.29862
user_001 Jumping 1.44604722793e12 1.87829 -1.91542 0.880768
user_001 Jumping 1.446047227995e12 1.57173 -5.86241 -3.75599
user_001 Jumping 1.446047228059e12 3.41111 -17.93331 0.535886
user_001 Jumping 1.446047228123e12 3.18118 -19.58108 5.74745
user_001 Jumping 1.446047228189e12 7.85626 -19.2362 0.804128
user_001 Jumping 1.446047228253e12 1.26517 -8.85139 2.18366
user_001 Jumping 1.446047228318e12 7.7239e-2 1.15021 1.53221
user_001 Jumping 1.446047228383e12 0.230521 2.0699 -1.41845
user_001 Jumping 1.446047228447e12 0.652044 -0.497565 1.76214
user_001 Jumping 1.446047228512e12 1.53341 -0.305964 1.41725
user_001 Jumping 1.446047228578e12 -1.07237 -1.95374 0.191003
user_001 Jumping 1.446047228642e12 2.75966 -13.75639 0.191003
user_001 Jumping 1.446047228707e12 7.43474 -19.58108 2.95007
user_001 Jumping 1.446047228771e12 5.63368 -19.58108 5.59417
user_001 Jumping 1.446047228836e12 5.02056 -11.72542 -1.38013
user_001 Jumping 1.4460472289e12 -2.10702 0.575403 1.07237
user_001 Jumping 1.446047228966e12 -1.30229 2.2615 -1.26517
user_001 Jumping 1.44604722903e12 1.68669 -0.957409 1.57053
user_001 Jumping 1.446047229095e12 2.60638 -0.229323 2.14534
user_001 Jumping 1.446047229159e12 1.30349 -0.152682 0.497565
user_001 Jumping 1.446047229224e12 1.64837 -8.12331 1.60885
user_001 Jumping 1.44604722929e12 0.15388 -18.46979 -1.03525
user_001 Jumping 1.446047229354e12 4.98224 -19.58108 0.995729
user_001 Jumping 1.446047229419e12 5.17384 -19.2362 0.612526
user_001 Jumping 1.446047229483e12 2.03158 -9.11964 1.34061
user_001 Jumping 1.446047229549e12 -1.95374 -1.03405 0.574206
user_001 Jumping 1.446047229612e12 0.1922 1.30349 -1.03525
user_001 Jumping 1.446047229678e12 1.64837 -0.727487 -0.307161
user_001 Jumping 1.446047229743e12 2.56806 -1.03405 0.267643
user_001 Jumping 1.446047229806e12 1.41845 -0.305964 0.727487
user_001 Jumping 1.446047229872e12 1.03525 -6.82042 0.957409
user_001 Jumping 1.446047229936e12 3.94759 -19.31284 -1.22685
user_001 Jumping 1.446047230001e12 6.13185 -19.58108 2.72014
user_001 Jumping 1.446047230066e12 7.89458 -16.9753 0.229323
user_001 Jumping 1.446047230131e12 2.6447 -3.75479 0.114362
user_001 Jumping 1.446047230195e12 -2.41358 1.91661 -5.99e-4
user_001 Jumping 1.44604723026e12 -1.95374 -0.114362 -0.268841
user_001 Jumping 1.446047230325e12 -0.229323 -1.95374 2.75846
user_001 Jumping 1.44604723039e12 2.68302 0.268841 0.535886
user_001 Jumping 1.446047230455e12 1.15021 -1.41725 0.880768
user_001 Jumping 1.446047230519e12 2.98958 -11.53382 -0.920286
user_001 Jumping 1.446047230584e12 8.00954 -19.58108 -0.1922
user_001 Jumping 1.446047230649e12 7.31978 -19.58108 2.52854
user_001 Jumping 1.446047230713e12 5.44208 -13.56479 -0.498763
user_001 Jumping 1.446047230779e12 0.728685 -0.420925 1.68549
user_001 Jumping 1.446047230842e12 1.18853 1.41845 -2.22318
user_001 Jumping 1.446047230907e12 0.15388 -1.80046 2.03038
user_001 Jumping 1.446047230972e12 -3.7722e-2 1.07357 -0.958607
user_001 Jumping 1.446047231038e12 0.230521 0.728685 -0.690364
user_001 Jumping 1.446047231102e12 0.805325 -1.14901 1.53221
user_001 Jumping 1.446047231167e12 5.17384 -9.15796 -2.91294
user_001 Jumping 1.446047231231e12 8.00954 -19.54276 1.49389
user_001 Jumping 1.446047231296e12 11.61165 -19.58108 4.25296
user_001 Jumping 1.446047231361e12 7.89458 -18.35483 3.71647
user_001 Jumping 1.446047231426e12 0.537083 -3.21831 0.420925
user_001 Jumping 1.44604723149e12 -1.91542 4.10087 -2.6447
user_001 Jumping 1.446047231555e12 -0.919089 -0.382604 0.114362
user_001 Jumping 1.44604723162e12 0.613724 -0.842448 1.57053
user_001 Jumping 1.446047231684e12 1.38013 -0.459245 0.305964
user_001 Jumping 1.446047231749e12 2.29982 -1.49389 -1.26517
user_001 Jumping 1.446047231814e12 4.94392 -10.95901 -0.498763
user_001 Jumping 1.446047231878e12 3.75599 -19.27452 -1.76333
user_001 Jumping 1.446047231944e12 7.70298 -19.58108 -2.95126
user_001 Jumping 1.446047232008e12 6.55337 -17.51178 -1.91661
user_001 Jumping 1.446047232073e12 2.10822 -2.03038 -0.268841
user_001 Jumping 1.446047232138e12 -1.68549 3.67935 -0.881966
user_001 Jumping 1.446047232203e12 0.15388 -0.114362 7.6042e-2
user_001 Jumping 1.446047232267e12 2.79798 -1.95374 0.689167
user_001 Jumping 1.446047232332e12 1.45677 -0.957409 0.420925
user_001 Jumping 1.446047232397e12 1.18853 -2.95007 0.650847
user_001 Jumping 1.446047232462e12 3.44943 -13.87135 -3.71767
user_001 Jumping 1.446047232526e12 3.79431 -19.58108 -0.345482
user_001 Jumping 1.446047232591e12 6.09353 -19.58108 2.87342
user_001 Jumping 1.446047232655e12 4.48408 -14.3312 -0.498763
user_001 Jumping 1.44604723272e12 -3.7722e-2 -1.68549 2.6435
user_001 Jumping 1.446047232785e12 0.613724 2.68302 -2.37646
user_001 Jumping 1.44604723285e12 0.996927 -0.497565 0.497565
user_001 Jumping 1.446047232915e12 0.15388 -0.689167 1.34061
user_001 Jumping 1.446047232979e12 1.07357 1.07357 -2.60638
user_001 Jumping 1.446047233044e12 2.37646 -3.29495 -1.45677
user_001 Jumping 1.446047233109e12 2.22318 -16.09393 1.37893
user_001 Jumping 1.446047233173e12 6.82161 -19.58108 3.7722e-2
user_001 Jumping 1.446047233238e12 8.39275 -19.54276 1.22565
user_001 Jumping 1.446047233303e12 1.22685 -9.50284 -0.307161
user_001 Jumping 1.446047233368e12 1.83997 -0.152682 1.41725
user_001 Jumping 1.446047233432e12 -0.765807 0.996927 -1.91661
user_001 Jumping 1.446047233497e12 0.728685 -0.612526 0.152682
user_001 Jumping 1.446047233562e12 0.996927 -0.305964 0.995729
user_001 Jumping 1.446047233626e12 1.22685 -0.305964 3.7722e-2
user_001 Jumping 1.446047233692e12 1.91661 -2.95007 -0.345482
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user_001 Jumping 1.446047234986e12 5.36544 -4.09967 -0.537083
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user_001 Jumping 1.446047235439e12 1.03525 -1.80046 1.64717
user_001 Jumping 1.446047235504e12 1.95493 -0.689167 1.49389
user_001 Jumping 1.446047235569e12 1.26517 0.383802 -0.307161
user_001 Jumping 1.446047235633e12 1.18853 -2.72014 1.41725
user_001 Jumping 1.446047235698e12 5.71033 -16.51545 -2.03158
user_001 Jumping 1.446047235763e12 6.55337 -19.58108 0.995729
user_001 Jumping 1.446047235828e12 10.577 -19.4278 -1.57173
user_001 Jumping 1.446047235892e12 2.79798 -9.88604 -0.843646
user_001 Jumping 1.446047235957e12 0.652044 -3.7722e-2 1.14901
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user_001 Jumping 1.446047236086e12 0.15388 -0.305964 0.995729
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user_001 Jumping 1.446047236346e12 7.05154 -17.97163 -1.61005
user_001 Jumping 1.44604723641e12 9.46572 -19.58108 2.10702
user_001 Jumping 1.446047236475e12 7.58802 -18.54643 3.10335
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user_001 Jumping 1.446047237122e12 5.97857 -17.78002 0.344284
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user_001 Jumping 1.446047237381e12 1.30349 -0.152682 1.45557
user_001 Jumping 1.446047237446e12 2.79798 5.99e-4 -0.460442
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user_001 Jumping 1.446047237575e12 3.90927 -6.62882 -1.49509
user_001 Jumping 1.44604723764e12 4.98224 -19.27452 1.57053
user_001 Jumping 1.446047237705e12 12.22478 -19.58108 2.0687
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user_001 Jumping 1.446047238352e12 10.53868 -19.58108 0.919089
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user_001 Jumping 1.446047238676e12 1.95493 0.230521 1.60885
user_001 Jumping 1.446047238741e12 0.920286 0.537083 -0.422122
user_001 Jumping 1.446047238806e12 5.99e-4 -0.650847 0.497565
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user_001 Jumping 1.446047239e12 10.50036 -19.58108 1.91542
user_001 Jumping 1.446047239064e12 8.16283 -19.58108 1.95374
user_001 Jumping 1.446047239129e12 3.56439 -9.4262 -1.22685
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user_001 Jumping 1.446047239388e12 1.99325 -0.191003 0.957409
user_001 Jumping 1.446047239453e12 1.26517 -0.305964 -5.99e-4
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user_001 Jumping 1.446047239647e12 9.58068 -19.58108 1.53221
user_001 Jumping 1.446047239712e12 8.04786 -19.2362 2.0687
user_001 Jumping 1.446047239777e12 1.80165 -6.01569 -0.422122
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user_001 Jumping 1.446047239971e12 1.45677 -0.880768 2.2603
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user_001 Jumping 1.446047240295e12 7.39642 -19.58108 1.11069
user_001 Jumping 1.44604724036e12 10.23212 -19.58108 0.459245
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user_001 Jumping 1.446047240618e12 0.268841 -1.91542 3.06503
user_001 Jumping 1.446047240683e12 1.72501 -0.535886 1.83878
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user_001 Jumping 1.446047240813e12 0.920286 -0.535886 -1.91661
user_001 Jumping 1.446047240878e12 4.40743 -11.61046 0.459245
user_001 Jumping 1.446047240941e12 6.78329 -19.58108 4.82776
user_001 Jumping 1.446047241007e12 9.35075 -19.58108 5.74745
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user_002 Standing 1.446309443517e12 -2.03038 -9.31124 -3.8919e-2
user_002 Standing 1.446309443582e12 -2.14534 -9.2346 -3.8919e-2
user_002 Standing 1.446309443647e12 -2.29862 -9.19628 -5.99e-4
user_002 Standing 1.446309443711e12 -2.29862 -9.19628 3.7722e-2
user_002 Standing 1.446309443776e12 -2.18366 -9.2346 -3.8919e-2
user_002 Standing 1.446309443841e12 -2.10702 -9.19628 3.7722e-2
user_002 Standing 1.446309443906e12 -2.10702 -9.15796 3.7722e-2
user_002 Standing 1.446309443971e12 -2.29862 -9.15796 0.114362
user_002 Standing 1.446309444036e12 -2.03038 -9.27292 -5.99e-4
user_002 Standing 1.4463094441e12 -2.10702 -9.19628 7.6042e-2
user_002 Standing 1.446309444165e12 -2.14534 -9.2346 3.7722e-2
user_002 Standing 1.44630944423e12 -2.22198 -9.19628 7.6042e-2
user_002 Standing 1.446309444295e12 -2.33694 -9.19628 0.191003
user_002 Standing 1.446309444359e12 -2.10702 -9.31124 0.114362
user_002 Standing 1.446309444424e12 -2.0687 -9.2346 -5.99e-4
user_002 Standing 1.446309444489e12 -2.03038 -9.2346 0.114362
user_002 Standing 1.446309444554e12 -2.41358 -9.00468 0.191003
user_002 Standing 1.446309444618e12 -2.37526 -9.19628 0.267643
user_002 Standing 1.446309444683e12 -2.14534 -9.2346 7.6042e-2
user_002 Standing 1.446309444748e12 -2.0687 -9.27292 7.6042e-2
user_002 Standing 1.446309444812e12 -2.33694 -9.2346 0.229323
user_002 Standing 1.446309444877e12 -2.2603 -9.19628 0.229323
user_002 Standing 1.446309444941e12 -2.18366 -9.2346 0.152682
user_002 Standing 1.446309445007e12 -2.22198 -9.2346 0.229323
user_002 Standing 1.446309445072e12 -2.22198 -9.15796 0.191003
user_002 Standing 1.446309445137e12 -2.10702 -9.27292 0.191003
user_002 Standing 1.446309445202e12 -2.10702 -9.31124 0.191003
user_002 Standing 1.446309445265e12 -1.91542 -9.34956 0.191003
user_002 Standing 1.446309445331e12 -1.83878 -9.2346 0.191003
user_002 Standing 1.446309445395e12 -1.91542 -9.08132 0.305964
user_002 Standing 1.446309445459e12 -1.95374 -9.19628 0.152682
user_002 Standing 1.446309445525e12 -1.83878 -9.34956 7.6042e-2
user_002 Standing 1.44630944559e12 -1.80046 -9.31124 7.6042e-2
user_002 Standing 1.446309445654e12 -1.68549 -9.38788 0.267643
user_002 Standing 1.446309445719e12 -1.80046 -9.19628 0.267643
user_002 Standing 1.446309445784e12 -1.76214 -9.34956 -5.99e-4
user_002 Standing 1.446309445849e12 -1.91542 -9.2346 0.152682
user_002 Standing 1.446309445913e12 -1.80046 -9.27292 0.152682
user_002 Standing 1.446309445978e12 -1.76214 -9.27292 0.152682
user_002 Standing 1.446309446043e12 -1.83878 -9.31124 0.152682
user_002 Standing 1.446309446108e12 -1.83878 -9.2346 0.152682
user_002 Standing 1.446309446173e12 -1.8771 -9.27292 0.229323
user_002 Standing 1.446309446237e12 -1.8771 -9.27292 0.229323
user_002 Standing 1.446309446302e12 -1.8771 -9.2346 0.191003
user_002 Standing 1.446309446367e12 -1.8771 -9.31124 0.191003
user_002 Standing 1.446309446432e12 -1.8771 -9.31124 0.152682
user_002 Standing 1.446309446496e12 -1.91542 -9.27292 0.191003
user_002 Standing 1.446309446561e12 -1.8771 -9.2346 0.229323
user_002 Standing 1.446309446625e12 -1.83878 -9.27292 0.152682
user_002 Standing 1.446309446691e12 -1.91542 -9.27292 7.6042e-2
user_002 Standing 1.446309446755e12 -1.8771 -9.31124 0.267643
user_002 Standing 1.44630944682e12 -1.80046 -9.27292 0.267643
user_002 Standing 1.446309446884e12 -1.80046 -9.27292 0.152682
user_002 Standing 1.44630944695e12 -1.72382 -9.31124 7.6042e-2
user_002 Standing 1.446309447014e12 -1.68549 -9.31124 7.6042e-2
user_002 Standing 1.446309447079e12 -1.83878 -9.31124 0.267643
user_002 Standing 1.446309447144e12 -1.8771 -9.27292 0.152682
user_002 Standing 1.446309447209e12 -1.76214 -9.19628 0.152682
user_002 Standing 1.446309447273e12 -1.72382 -9.27292 0.152682
user_002 Standing 1.446309447338e12 -1.83878 -9.27292 0.267643
user_002 Standing 1.446309447403e12 -1.8771 -9.31124 0.229323
user_002 Standing 1.446309447467e12 -1.83878 -9.31124 7.6042e-2
user_002 Standing 1.446309447532e12 -1.68549 -9.34956 7.6042e-2
user_002 Standing 1.446309447597e12 -1.68549 -9.34956 0.152682
user_002 Standing 1.446309447662e12 -1.72382 -9.2346 0.191003
user_002 Standing 1.446309447726e12 -1.8771 -9.31124 0.152682
user_002 Standing 1.446309447791e12 -1.80046 -9.31124 0.152682
user_002 Standing 1.446309447855e12 -1.64717 -9.31124 0.114362
user_002 Standing 1.446309447921e12 -1.60885 -9.27292 0.114362
user_002 Standing 1.446309447986e12 -1.68549 -9.27292 0.229323
user_002 Standing 1.44630944805e12 -1.76214 -9.34956 0.191003
user_002 Standing 1.446309448115e12 -1.72382 -9.34956 0.191003
user_002 Standing 1.44630944818e12 -1.72382 -9.27292 0.267643
user_002 Standing 1.446309448245e12 -1.64717 -9.31124 0.229323
user_002 Standing 1.446309448309e12 -1.64717 -9.27292 0.152682
user_002 Standing 1.446309448374e12 -1.72382 -9.31124 0.229323
user_002 Standing 1.446309448439e12 -1.72382 -9.34956 0.267643
user_002 Standing 1.446309448504e12 -1.72382 -9.2346 0.191003
user_002 Standing 1.446309448569e12 -1.64717 -9.31124 0.152682
user_002 Standing 1.446309448633e12 -1.72382 -9.27292 0.191003
user_002 Standing 1.446309448698e12 -1.68549 -9.27292 0.191003
user_002 Standing 1.446309448763e12 -1.68549 -9.27292 0.152682
user_002 Standing 1.446309448827e12 -1.64717 -9.31124 0.267643
user_002 Standing 1.446309448892e12 -1.64717 -9.34956 0.229323
user_002 Standing 1.446309448957e12 -1.60885 -9.31124 7.6042e-2
user_002 Standing 1.446309449022e12 -1.60885 -9.34956 0.152682
user_002 Standing 1.446309449087e12 -1.68549 -9.31124 0.229323
user_002 Standing 1.446309449151e12 -1.76214 -9.27292 0.229323
user_002 Standing 1.446309449216e12 -1.68549 -9.31124 0.152682
user_002 Standing 1.446309449281e12 -1.68549 -9.31124 7.6042e-2
user_002 Standing 1.446309449346e12 -1.72382 -9.2346 0.191003
user_002 Standing 1.44630944941e12 -1.64717 -9.34956 0.267643
user_002 Standing 1.446309449475e12 -1.76214 -9.27292 0.191003
user_002 Standing 1.44630944954e12 -1.64717 -9.31124 -5.99e-4
user_002 Standing 1.446309449605e12 -1.64717 -9.31124 0.229323
user_002 Standing 1.446309449669e12 -1.68549 -9.27292 0.229323
user_002 Standing 1.446309449734e12 -1.68549 -9.31124 7.6042e-2
user_002 Standing 1.446309449799e12 -1.76214 -9.31124 0.114362
user_002 Standing 1.446309449864e12 -1.76214 -9.27292 0.229323
user_002 Standing 1.446309449928e12 -1.72382 -9.31124 0.229323
user_002 Standing 1.446309449993e12 -1.72382 -9.34956 0.152682
user_002 Standing 1.446309450057e12 -1.72382 -9.34956 0.114362
user_002 Standing 1.446309450123e12 -1.72382 -9.31124 0.267643
user_002 Standing 1.446309450188e12 -1.68549 -9.34956 0.152682
user_002 Standing 1.446309450252e12 -1.83878 -9.31124 0.114362
user_002 Standing 1.446309450317e12 -1.68549 -9.34956 0.191003
user_002 Standing 1.446309450381e12 -1.72382 -9.31124 0.191003
user_002 Standing 1.446309450446e12 -1.68549 -9.34956 3.7722e-2
user_002 Standing 1.446309450511e12 -1.68549 -9.27292 0.229323
user_002 Standing 1.446309450576e12 -1.76214 -9.31124 0.229323
user_002 Standing 1.446309450641e12 -1.72382 -9.31124 0.152682
user_002 Standing 1.446309450705e12 -1.64717 -9.27292 0.152682
user_002 Standing 1.44630945077e12 -1.72382 -9.34956 0.114362
user_002 Standing 1.446309450835e12 -1.83878 -9.2346 0.191003
dataDF.count()
res5: Long = 13679
dataDF.select($"user_id").distinct().show()
+--------+
| user_id|
+--------+
|user_002|
|user_006|
|user_005|
|user_001|
|user_007|
|user_003|
|user_004|
+--------+
dataDF.select($"activity").distinct().show()
+--------+
|activity|
+--------+
| Sitting|
| Walking|
| Jumping|
|Standing|
| Jogging|
+--------+
val sDF = dataDF.sample(false,0.105, 12345L)
sDF.count
sDF: org.apache.spark.sql.Dataset[org.apache.spark.sql.Row] = [user_id: string, activity: string ... 4 more fields]
res8: Long = 1427
sDF.show(5)
+--------+--------+---------------+--------+---------+--------+
| user_id|activity|timeStampAsLong|       x|        y|       z|
+--------+--------+---------------+--------+---------+--------+
|user_001| Jumping|  1446047227671|0.575403|-0.727487| 2.95007|
|user_001| Jumping|  1446047228253| 1.26517| -8.85139| 2.18366|
|user_001| Jumping|  1446047228836| 5.02056|-11.72542|-1.38013|
|user_001| Jumping|  1446047229354| 4.98224|-19.58108|0.995729|
|user_001| Jumping|  1446047229419| 5.17384| -19.2362|0.612526|
+--------+--------+---------------+--------+---------+--------+
only showing top 5 rows
sDF.show(5)
+--------+--------+---------------+--------+---------+--------+
| user_id|activity|timeStampAsLong|       x|        y|       z|
+--------+--------+---------------+--------+---------+--------+
|user_001| Jumping|  1446047227671|0.575403|-0.727487| 2.95007|
|user_001| Jumping|  1446047228253| 1.26517| -8.85139| 2.18366|
|user_001| Jumping|  1446047228836| 5.02056|-11.72542|-1.38013|
|user_001| Jumping|  1446047229354| 4.98224|-19.58108|0.995729|
|user_001| Jumping|  1446047229419| 5.17384| -19.2362|0.612526|
+--------+--------+---------------+--------+---------+--------+
only showing top 5 rows
display(dataDF.sample(false,0.1))
user_id activity timeStampAsLong x y z
user_001 Jumping 1.446047227799e12 0.690364 -3.7722e-2 1.72382
user_001 Jumping 1.44604722793e12 1.87829 -1.91542 0.880768
user_001 Jumping 1.446047227995e12 1.57173 -5.86241 -3.75599
user_001 Jumping 1.446047228383e12 0.230521 2.0699 -1.41845
user_001 Jumping 1.446047228512e12 1.53341 -0.305964 1.41725
user_001 Jumping 1.446047228707e12 7.43474 -19.58108 2.95007
user_001 Jumping 1.446047228966e12 -1.30229 2.2615 -1.26517
user_001 Jumping 1.446047230195e12 -2.41358 1.91661 -5.99e-4
user_001 Jumping 1.446047230584e12 8.00954 -19.58108 -0.1922
user_001 Jumping 1.446047231296e12 11.61165 -19.58108 4.25296
user_001 Jumping 1.446047233562e12 0.996927 -0.305964 0.995729
user_001 Jumping 1.44604723421e12 2.79798 -0.114362 0.919089
user_001 Jumping 1.446047234468e12 6.89825 -19.58108 -4.25415
user_001 Jumping 1.446047234663e12 0.805325 1.15021 -0.15388
user_001 Jumping 1.446047234986e12 5.36544 -4.09967 -0.537083
user_001 Jumping 1.446047235115e12 6.93658 -19.58108 -2.75966
user_001 Jumping 1.446047235633e12 1.18853 -2.72014 1.41725
user_001 Jumping 1.446047235763e12 6.55337 -19.58108 0.995729
user_001 Jumping 1.446047236281e12 3.56439 -5.90073 0.727487
user_001 Jumping 1.446047236346e12 7.05154 -17.97163 -1.61005
user_001 Jumping 1.446047236669e12 0.11556 -0.114362 -1.11189
user_001 Jumping 1.446047236798e12 1.80165 0.345482 0.765807
user_001 Jumping 1.446047236928e12 3.48775 -7.31858 -0.728685
user_001 Jumping 1.446047236992e12 5.32712 -18.92964 0.114362
user_001 Jumping 1.446047237057e12 10.34708 -19.58108 2.37526
user_001 Jumping 1.44604723764e12 4.98224 -19.27452 1.57053
user_001 Jumping 1.446047238287e12 6.32345 -17.62674 -0.728685
user_001 Jumping 1.446047238676e12 1.95493 0.230521 1.60885
user_001 Jumping 1.446047241849e12 -0.919089 2.6447 -3.14286
user_001 Jumping 1.446047243725e12 -1.07237 1.15021 0.152682
user_001 Jumping 1.446047243984e12 2.87462 -0.535886 -0.268841
user_001 Jumping 1.446047244243e12 14.86888 -19.58108 -1.41845
user_003 Jumping 1.446047778293e12 -3.63983 -9.04299 -2.6447
user_003 Jumping 1.446047780171e12 -3.37159 -5.78577 -3.87095
user_003 Jumping 1.446047780365e12 -3.86975 -19.58108 -5.40376
user_003 Jumping 1.446047781725e12 0.230521 0.268841 -0.345482
user_003 Jumping 1.446047782244e12 -1.45557 -7.85507 -1.22685
user_003 Jumping 1.446047782373e12 -1.64717 -5.90073 -2.33814
user_003 Jumping 1.446047783151e12 -1.14901 -14.98264 -4.13919
user_003 Jumping 1.446047783409e12 -3.67815 -4.44456 -2.4531
user_003 Jumping 1.446047784057e12 -2.8351 -17.62674 -5.02056
user_003 Jumping 1.44604778451e12 -0.344284 -6.51385 -2.8363
user_003 Jumping 1.446047784575e12 -4.02303 -14.98264 -2.2615
user_003 Jumping 1.446047784769e12 -2.4519 7.7239e-2 1.11069
user_003 Jumping 1.446047785158e12 -4.3296 -19.38948 -5.17384
user_003 Jumping 1.446047785287e12 -3.44823 -7.24194 -2.18486
user_003 Jumping 1.44604778587e12 -0.919089 -4.82776 -0.268841
user_003 Jumping 1.446047786129e12 -0.842448 -0.497565 -3.0279
user_003 Jumping 1.446047786453e12 -3.94639 -5.59417 -3.14286
user_003 Jumping 1.44604778723e12 -0.880768 0.422122 -1.03525
user_003 Jumping 1.446047787358e12 -4.59784 -19.35116 -5.94025
user_003 Jumping 1.446047787553e12 -3.44823 -6.47553 -2.75966
user_003 Jumping 1.446047788136e12 -3.14167 2.72134 -0.575403
user_003 Jumping 1.446047788719e12 -2.10702 -7.31858 -2.10822
user_003 Jumping 1.446047789301e12 0.843646 -0.382604 1.11069
user_003 Jumping 1.446047789495e12 -3.90807 -17.74171 -7.58802
user_003 Jumping 1.446047789818e12 -2.03038 -6.85874 -1.68669
user_003 Jumping 1.446047790078e12 -5.51753 -19.58108 -7.24314
user_003 Jumping 1.446047790726e12 -1.26397 -8.12331 -3.10454
user_003 Jumping 1.446047790919e12 -1.83878 -3.40991 -3.60271
user_003 Jumping 1.446047791114e12 -7.70178 -19.58108 -7.5497
user_003 Jumping 1.446047791762e12 -2.14534 -9.84772 -3.2195
user_003 Jumping 1.446047792021e12 -2.95007 -5.096 -2.52974
user_003 Jumping 1.446047792669e12 -2.87342 -18.96796 -5.86361
user_003 Jumping 1.446047793834e12 -3.52487 -13.87135 -5.63368
user_003 Jumping 1.446047794158e12 -1.57053 -5.90073 -3.2195
user_002 Standing 1.446309439342e12 -2.49022 -9.19628 -1.11189
user_002 Standing 1.446309439373e12 -2.75846 -9.08132 -1.15021
user_002 Standing 1.446309439584e12 -2.52854 -8.88971 -1.15021
user_002 Standing 1.446309439665e12 -2.8351 -9.2346 -0.920286
user_002 Standing 1.446309439924e12 -3.10335 -8.77475 -0.690364
user_002 Standing 1.446309440021e12 -2.91174 -9.08132 -1.22685
user_002 Standing 1.446309440045e12 -3.06503 -9.00468 -1.03525
user_002 Standing 1.446309440111e12 -3.10335 -9.00468 -0.881966
user_002 Standing 1.446309440167e12 -3.33327 -8.85139 -0.613724
user_002 Standing 1.446309440239e12 -3.14167 -8.88971 -0.805325
user_002 Standing 1.446309440426e12 -3.21831 -8.88971 -0.728685
user_002 Standing 1.446309440498e12 -3.33327 -8.96635 -0.805325
user_002 Standing 1.446309440604e12 -2.87342 -8.85139 -0.652044
user_002 Standing 1.446309440717e12 -3.06503 -8.88971 -0.383802
user_002 Standing 1.446309440887e12 -3.17999 -8.96635 -0.345482
user_002 Standing 1.446309440951e12 -3.21831 -8.85139 -0.575403
user_002 Standing 1.446309440976e12 -3.17999 -8.81307 -0.728685
user_002 Standing 1.446309441017e12 -2.91174 -9.08132 -0.652044
user_002 Standing 1.446309441049e12 -2.87342 -9.04299 -0.575403
user_002 Standing 1.446309441276e12 -3.29495 -8.81307 -0.498763
user_002 Standing 1.446309441341e12 -3.37159 -9.08132 -0.460442
user_002 Standing 1.446309441349e12 -3.44823 -9.00468 -0.383802
user_002 Standing 1.446309441453e12 -3.29495 -8.85139 -0.345482
user_002 Standing 1.446309441501e12 -3.29495 -9.00468 -0.383802
user_002 Standing 1.446309441591e12 -3.40991 -8.73643 -0.230521
user_002 Standing 1.446309441615e12 -3.40991 -8.77475 -0.345482
user_002 Standing 1.446309441664e12 -3.17999 -9.2346 -0.460442
user_002 Standing 1.446309441688e12 -3.29495 -9.19628 -0.422122
user_002 Standing 1.446309441793e12 -3.17999 -9.2346 -0.307161
user_002 Standing 1.446309441842e12 -3.17999 -8.88971 -0.537083
user_002 Standing 1.446309441882e12 -3.29495 -8.85139 -0.345482
user_002 Standing 1.446309441907e12 -3.17999 -8.77475 -0.230521
user_002 Standing 1.446309441915e12 -3.17999 -9.08132 -3.8919e-2
user_002 Standing 1.446309441979e12 -3.25663 -9.08132 -0.268841
user_002 Standing 1.446309442085e12 -2.98839 -9.00468 -5.99e-4
user_002 Standing 1.446309442287e12 -2.87342 -9.08132 -0.268841
user_002 Standing 1.446309442417e12 -2.56686 -9.19628 -3.8919e-2
user_002 Standing 1.446309443323e12 -2.2603 -9.19628 -0.11556
user_002 Standing 1.446309443776e12 -2.18366 -9.2346 -3.8919e-2
user_002 Standing 1.446309444036e12 -2.03038 -9.27292 -5.99e-4
user_002 Standing 1.446309444165e12 -2.14534 -9.2346 3.7722e-2
user_002 Standing 1.446309444295e12 -2.33694 -9.19628 0.191003
user_002 Standing 1.446309444424e12 -2.0687 -9.2346 -5.99e-4
user_002 Standing 1.44630944805e12 -1.76214 -9.34956 0.191003
user_002 Standing 1.446309448763e12 -1.68549 -9.27292 0.152682
user_002 Standing 1.446309449151e12 -1.76214 -9.27292 0.229323
user_002 Standing 1.446309449346e12 -1.72382 -9.2346 0.191003
user_002 Standing 1.446309449993e12 -1.72382 -9.34956 0.152682
user_002 Standing 1.446309450317e12 -1.68549 -9.34956 0.191003
user_002 Standing 1.446309450576e12 -1.76214 -9.31124 0.229323
user_002 Standing 1.446309450835e12 -1.83878 -9.2346 0.191003
user_002 Standing 1.446309452195e12 -1.76214 -9.27292 0.191003
user_002 Standing 1.446309452389e12 -1.72382 -9.34956 0.191003
user_002 Standing 1.446309452907e12 -1.72382 -9.27292 0.229323
user_002 Standing 1.446309453685e12 -1.76214 -9.19628 0.191003
user_002 Standing 1.446309453749e12 -1.68549 -9.31124 0.229323
user_002 Standing 1.446309454915e12 -1.76214 -9.27292 0.267643
user_002 Standing 1.446309455109e12 -1.80046 -9.2346 0.152682
user_002 Standing 1.446309455239e12 -1.72382 -9.31124 0.191003
user_002 Standing 1.446309455562e12 -1.68549 -9.27292 0.114362
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user_002 Jogging 1.446034911571e12 4.13919 -1.03405 -1.87829
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user_002 Jogging 1.446034914678e12 -3.67815 0.345482 2.2603
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user_005 Jumping 1.446046632766e12 -2.75846 -3.60151 1.37893
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user_005 Jumping 1.446046634515e12 1.87829 2.03158 3.21831
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user_005 Jumping 1.446046637493e12 9.69564 -19.58108 -10.61533
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user_005 Jumping 1.446046640277e12 3.25783 -19.58108 -10.76861
user_005 Jumping 1.446046640342e12 6.78329 -19.35116 -4.63736
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user_005 Jumping 1.44604664112e12 -1.8771 0.460442 -3.94759
user_005 Jumping 1.44604664209e12 3.0279 -10.53749 -5.90193
user_005 Jumping 1.44604664235e12 -2.68182 -3.7722e-2 -3.60271
user_005 Jumping 1.446046642674e12 -2.03038 -2.98839 1.37893
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user_005 Jumping 1.446046644551e12 1.30349 -2.22198 2.29862
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user_002 Jumping 1.446035036129e12 -0.114362 0.996927 -3.8919e-2
user_002 Jumping 1.446035036582e12 -10.80573 -14.94432 1.22565
user_002 Jumping 1.446035036647e12 -0.459245 -2.14534 -0.767005
user_002 Jumping 1.44603503736e12 0.268841 -0.995729 -0.958607
user_002 Jumping 1.446035038783e12 -9.88604 -13.48815 0.574206
user_002 Jumping 1.446035040338e12 5.99e-4 -1.07237 -0.1922
user_002 Jumping 1.446035040531e12 -9.65612 -12.60678 -1.15021
user_002 Jumping 1.446035043056e12 -12.41518 -19.08292 -2.2615
user_002 Jumping 1.446035043121e12 -4.3296 -6.74378 0.114362
user_002 Jumping 1.446035043962e12 -1.76214 -0.919089 -1.38013
user_002 Jumping 1.446035044415e12 0.268841 1.68669 -1.57173
user_002 Jumping 1.446035044609e12 -1.41725 -1.45557 -1.38013
user_002 Jumping 1.446035044868e12 -11.57214 -16.5921 -0.498763
user_002 Jumping 1.446035046228e12 -7.6042e-2 0.307161 -7.7239e-2
user_002 Jumping 1.446035046486e12 -13.21991 -15.71073 0.305964
user_002 Jumping 1.446035047263e12 -4.06135 -5.90073 -3.8919e-2
user_002 Jumping 1.446035048234e12 -12.83671 -15.0976 7.6042e-2
user_002 Jumping 1.446035049399e12 -13.52647 -17.3585 -0.958607
user_003 Sitting 1.446047526718e12 0.422122 -0.650847 9.4262
user_003 Sitting 1.446047527172e12 0.498763 -0.612526 9.46452
user_003 Sitting 1.446047528661e12 0.460442 -0.650847 9.4262
user_003 Sitting 1.446047529656e12 0.460442 -0.727487 9.4262
user_003 Sitting 1.446047529705e12 0.422122 -0.650847 9.69444
user_003 Sitting 1.446047529786e12 0.345482 -0.727487 9.34956
user_003 Sitting 1.446047529817e12 0.575403 -0.612526 9.34956
user_003 Sitting 1.446047529842e12 0.498763 -0.650847 9.31124
user_003 Sitting 1.44604752985e12 0.460442 -0.727487 9.46452
user_003 Sitting 1.446047529988e12 0.307161 -0.804128 9.38788
user_003 Sitting 1.446047530045e12 0.460442 -0.804128 9.4262
user_003 Sitting 1.446047530101e12 0.345482 -0.574206 9.4262
user_003 Sitting 1.446047530133e12 0.345482 -0.727487 9.50284
user_003 Sitting 1.446047530215e12 0.537083 -0.612526 9.46452
user_003 Sitting 1.446047530231e12 0.460442 -0.612526 9.54116
user_003 Sitting 1.446047530255e12 0.383802 -0.650847 9.4262
user_003 Sitting 1.446047530263e12 0.537083 -0.612526 9.46452
user_003 Sitting 1.446047530425e12 0.575403 -0.574206 9.50284
user_003 Sitting 1.446047530562e12 0.575403 -0.765807 9.46452
user_003 Sitting 1.446047530595e12 0.345482 -0.689167 9.31124
user_003 Sitting 1.44604753061e12 0.575403 -0.612526 9.4262
user_003 Sitting 1.4460475307e12 0.575403 -0.612526 9.4262
user_003 Sitting 1.446047530707e12 0.613724 -0.727487 9.38788
user_003 Sitting 1.446047530749e12 0.422122 -0.765807 9.4262
user_003 Sitting 1.446047530846e12 0.383802 -0.727487 9.4262
user_003 Sitting 1.446047530871e12 0.575403 -0.650847 9.46452
user_003 Sitting 1.446047530886e12 0.537083 -0.650847 9.34956
user_003 Sitting 1.446047530927e12 0.460442 -0.727487 9.50284
user_003 Sitting 1.446047531113e12 0.422122 -0.765807 9.50284
user_003 Sitting 1.44604753121e12 0.383802 -0.497565 9.34956
user_003 Sitting 1.446047531217e12 0.383802 -0.612526 9.38788
user_003 Sitting 1.446047531234e12 0.422122 -0.612526 9.38788
user_003 Sitting 1.446047531493e12 0.537083 -0.612526 9.4262
user_003 Sitting 1.446047531526e12 0.307161 -0.574206 9.46452
user_003 Sitting 1.446047531656e12 0.498763 -0.650847 9.38788
user_003 Sitting 1.446047531728e12 0.230521 -0.689167 9.50284
user_003 Sitting 1.446047531736e12 0.307161 -0.650847 9.4262
user_003 Sitting 1.446047531768e12 0.460442 -0.765807 9.50284
user_003 Sitting 1.446047531833e12 0.537083 -0.880768 9.38788
user_003 Sitting 1.446047531881e12 0.498763 -0.612526 9.38788
user_003 Sitting 1.446047531889e12 0.498763 -0.765807 9.4262
user_003 Sitting 1.446047531922e12 0.383802 -0.765807 9.38788
user_003 Sitting 1.44604753193e12 0.460442 -0.880768 9.46452
user_003 Sitting 1.446047531939e12 0.460442 -0.612526 9.54116
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user_003 Sitting 1.446047532043e12 0.460442 -0.612526 9.46452
user_003 Sitting 1.446047532108e12 0.575403 -0.612526 9.4262
user_003 Sitting 1.446047532237e12 0.422122 -0.574206 9.50284
user_003 Sitting 1.446047532724e12 0.460442 -0.727487 9.4262
user_003 Sitting 1.44604753278e12 0.460442 -0.535886 9.34956
user_003 Sitting 1.446047533443e12 0.498763 -0.650847 9.4262
user_003 Sitting 1.446047533702e12 0.422122 -0.650847 9.50284
user_003 Sitting 1.446047535127e12 0.422122 -0.689167 9.50284
user_003 Sitting 1.446047535386e12 0.498763 -0.689167 9.38788
user_003 Sitting 1.446047535904e12 0.422122 -0.689167 9.46452
user_003 Sitting 1.446047536033e12 0.460442 -0.650847 9.50284
user_003 Sitting 1.446047536227e12 0.422122 -0.650847 9.38788
user_003 Sitting 1.446047536745e12 0.460442 -0.650847 9.4262
user_003 Sitting 1.446047537781e12 0.460442 -0.612526 9.46452
user_003 Sitting 1.446047537963e12 2.91294 -4.06135 -17.7429
user_003 Sitting 1.44604753806e12 0.460442 -0.727487 9.34956
user_003 Sitting 1.446047538237e12 0.537083 -0.650847 9.46452
user_003 Sitting 1.446047538246e12 0.690364 -0.727487 9.46452
user_003 Sitting 1.44604753827e12 0.498763 -0.689167 9.54116
user_003 Sitting 1.446047538287e12 0.460442 -0.842448 9.54116
user_003 Sitting 1.446047538295e12 0.537083 -0.727487 9.57948
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user_003 Sitting 1.446047538448e12 0.345482 -0.727487 9.50284
user_003 Sitting 1.446047538529e12 0.460442 -0.650847 9.34956
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user_003 Sitting 1.446047540941e12 0.498763 -0.957409 9.54116
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user_003 Sitting 1.44604754111e12 0.575403 -0.535886 9.50284
user_003 Sitting 1.446047541135e12 0.460442 -0.650847 9.38788
user_003 Sitting 1.4460475412e12 0.498763 -0.689167 9.27292
user_003 Sitting 1.446047541223e12 0.307161 -0.689167 9.46452
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user_004 Walking 1.446046371124e12 0.230521 -9.08132 7.6042e-2
user_004 Walking 1.446046371189e12 -0.727487 -8.96635 1.14901
user_004 Walking 1.446046372095e12 -1.53221 -13.18159 5.51753
user_004 Walking 1.446046373391e12 -1.68549 -8.16163 1.72382
user_004 Walking 1.446046374038e12 -1.34061 -1.99206 -2.95126
user_004 Walking 1.446046376822e12 0.15388 -9.54116 -7.7239e-2
user_004 Walking 1.446046377082e12 1.41845 -13.25823 0.842448
user_004 Walking 1.44604637883e12 -3.44823 -2.2603 1.22565
user_004 Walking 1.446046379219e12 2.49142 -10.72909 -1.07357
user_004 Walking 1.446046379801e12 1.80165 -10.1926 -7.43474
user_004 Walking 1.446046379995e12 -4.98104 -6.59049 3.21831
user_004 Walking 1.446046380349e12 0.881966 -11.34221 -1.30349
user_004 Walking 1.446046380357e12 -0.229323 -11.03565 -1.91661
user_004 Walking 1.446046380616e12 2.60638 -8.65979 -1.18853
user_004 Walking 1.446046380632e12 1.91661 -9.04299 -1.95493
user_004 Walking 1.446046380802e12 -0.152682 -3.71647 -4.86728
user_004 Walking 1.446046380818e12 0.422122 -5.01936 -6.47673
user_004 Walking 1.446046380826e12 0.920286 -5.67081 -7.12818
user_004 Walking 1.446046380891e12 3.18118 -18.96796 -9.92556
user_004 Walking 1.446046380899e12 2.22318 -16.28553 -8.58435
user_004 Walking 1.446046381053e12 -3.52487 -1.76214 0.650847
user_004 Walking 1.446046381109e12 -2.6435 -10.26924 2.10702
user_004 Walking 1.446046381166e12 4.63736 -9.92436 -3.29615
user_004 Walking 1.446046381377e12 -1.26397 -8.96635 -0.307161
user_004 Walking 1.446046381393e12 -0.497565 -9.27292 -1.68669
user_004 Walking 1.4460463814e12 0.307161 -9.34956 -1.38013
user_004 Walking 1.446046381539e12 0.767005 -13.10495 1.45557
user_004 Walking 1.446046381708e12 3.41111 -8.62147 -2.49142
user_004 Walking 1.446046381757e12 0.958607 -7.58682 -0.307161
user_004 Walking 1.446046381773e12 -0.152682 -6.51385 7.6042e-2
user_004 Walking 1.446046381797e12 -1.72382 -4.7128 1.22565
user_004 Walking 1.446046381822e12 -3.06503 -2.98839 0.727487
user_004 Walking 1.446046381854e12 -3.29495 -2.03038 -1.41845
user_004 Walking 1.446046381886e12 -1.14901 -2.22198 -4.02423
user_004 Walking 1.446046381919e12 0.958607 -6.16897 -5.40376
user_004 Walking 1.446046381959e12 3.71767 -15.05928 -7.70298
user_004 Walking 1.446046382089e12 -3.71647 -10.72909 -2.14654
user_004 Walking 1.446046382129e12 -11.76374 -19.50444 -0.843646
user_004 Walking 1.44604638221e12 -4.09967 -3.40991 5.096
user_004 Walking 1.446046382259e12 0.652044 -19.58108 4.63616
user_004 Walking 1.446046382316e12 -0.229323 -4.82776 -0.575403
user_004 Walking 1.446046382332e12 -3.86975 -4.48288 2.14534
user_004 Walking 1.446046382526e12 1.49509 -9.77108 -0.537083
user_004 Walking 1.446046382566e12 3.2195 -10.95901 -7.7239e-2
user_004 Walking 1.446046382647e12 -0.152682 -13.79471 0.574206
user_004 Walking 1.44604638285e12 2.60638 -7.77842 -2.33814
user_004 Walking 1.446046383157e12 -0.344284 -11.61046 -6.82161
user_004 Walking 1.446046383174e12 -1.22565 -8.08499 -7.08986
user_004 Jumping 1.446046440495e12 -0.612526 -0.995729 -0.728685
user_004 Jumping 1.446046440559e12 1.41845 -0.880768 -7.7239e-2
user_004 Jumping 1.44604644069e12 8.35443 -7.66346 -0.460442
user_004 Jumping 1.446046441337e12 14.02583 -14.7144 -0.958607
user_004 Jumping 1.446046442243e12 0.575403 1.15021 -0.690364
user_004 Jumping 1.446046442502e12 6.89825 -11.11229 -1.57173
user_004 Jumping 1.446046443085e12 3.94759 -0.305964 1.30229
user_004 Jumping 1.446046444705e12 -1.72382 1.26517 -1.45677
user_004 Jumping 1.446046444899e12 0.498763 1.30349 1.18733
user_004 Jumping 1.446046445028e12 19.19908 -19.08292 -3.79431
user_004 Jumping 1.446046445093e12 3.18118 -8.46819 1.30229
user_004 Jumping 1.446046445352e12 1.61005 -0.689167 -0.613724
user_004 Jumping 1.446046445482e12 12.03318 -8.88971 -0.920286
user_004 Jumping 1.446046446387e12 1.30349 -1.57053 -1.76333
user_004 Jumping 1.446046446777e12 1.15021 6.40009 -2.41478
user_004 Jumping 1.446046446842e12 -1.41725 0.230521 -1.30349
user_004 Jumping 1.446046447036e12 0.498763 0.690364 -1.34181
user_004 Jumping 1.44604644723e12 -1.26397 -3.60151 4.40624
user_004 Jumping 1.446046448784e12 16.36337 -16.86034 -1.72501
user_004 Jumping 1.446046448849e12 -0.535886 -3.83143 4.63616
user_004 Jumping 1.446046449172e12 1.38013 2.56806 0.191003
user_004 Jumping 1.446046449949e12 -2.0687 0.575403 1.07237
user_004 Jumping 1.446046450079e12 -1.76214 -0.459245 -0.728685
user_004 Jumping 1.446046450273e12 1.03525 0.996927 -2.33814
user_004 Jumping 1.446046450726e12 0.805325 -3.7722e-2 -0.767005
user_004 Jumping 1.446046451115e12 0.268841 4.40743 -3.06622
user_004 Jumping 1.446046451503e12 17.62794 -14.63776 -3.41111
user_004 Jumping 1.446046451697e12 -1.80046 1.76333 -2.10822
user_004 Jumping 1.446046452086e12 3.37279 -10.34589 3.14167
user_004 Jumping 1.446046452409e12 0.690364 1.49509 -1.68669
user_004 Jumping 1.446046453575e12 -0.305964 0.690364 -1.07357
user_004 Jumping 1.446046455194e12 0.881966 1.87829 -0.575403

Feature Selection on Running Windows

  1. ETL Using SparkSQL Windows

A Markov Process Assumption

This is sensible since the subjects are not instantaneously changing between the activities of interest: sitting, walking, jogging, etc. Thus it makes sense to try and use the most recent accelerometer readings (from the immediate past) to predict the current activity.

 // Import the window functions.
import org.apache.spark.sql.expressions.Window
import org.apache.spark.sql.functions._

// Create a window specification
val windowSize = 10
val wSpec1 = Window.partitionBy("user_id","activity").orderBy("timeStampAsLong").rowsBetween(-windowSize, 0)
import org.apache.spark.sql.expressions.Window
import org.apache.spark.sql.functions._
windowSize: Int = 10
wSpec1: org.apache.spark.sql.expressions.WindowSpec = org.apache.spark.sql.expressions.WindowSpec@ade1233
 // Calculate the moving window statistics from data
val dataFeatDF = dataDF
      .withColumn( "meanX", mean($"x").over(wSpec1)  )
      .withColumn( "meanY", mean($"y").over(wSpec1)  )
      .withColumn( "meanZ", mean($"z").over(wSpec1)  ) 
//resultant = 1/n * ∑ √(x² + y² + z²)
      .withColumn( "SqX", pow($"x",2.0) )
      .withColumn( "SqY", pow($"y",2.0) )
      .withColumn( "SqZ", pow($"z",2.0) )
      .withColumn( "resultant", pow( $"SqX"+$"SqY"+$"SqZ",0.50 ) )
      .withColumn( "meanResultant", mean("resultant").over(wSpec1) )
// (1 / n ) * ∑ |b - mean_b|, for b in {x,y,z} 
      .withColumn( "absDevFromMeanX", abs($"x" - $"meanX") )
      .withColumn( "absDevFromMeanY", abs($"y" - $"meanY") )
      .withColumn( "absDevFromMeanZ", abs($"z" - $"meanZ") )
      .withColumn( "meanAbsDevFromMeanX", mean("absDevFromMeanX").over(wSpec1) )
      .withColumn( "meanAbsDevFromMeanY", mean("absDevFromMeanY").over(wSpec1) )
      .withColumn( "meanAbsDevFromMeanZ", mean("absDevFromMeanZ").over(wSpec1) )
//standard deviation  = √ variance = √ 1/n * ∑ (x - u)² with u = mean x
      .withColumn( "sqrDevFromMeanX", pow($"absDevFromMeanX",2.0) )
      .withColumn( "sqrDevFromMeanY", pow($"absDevFromMeanY",2.0) )
      .withColumn( "sqrDevFromMeanZ", pow($"absDevFromMeanZ",2.0) )
      .withColumn( "varianceX", mean("sqrDevFromMeanX").over(wSpec1) )
      .withColumn( "varianceY", mean("sqrDevFromMeanY").over(wSpec1) )
      .withColumn( "varianceZ", mean("sqrDevFromMeanZ").over(wSpec1) )
      .withColumn( "stddevX", pow($"varianceX",0.50) )
      .withColumn( "stddevY", pow($"varianceY",0.50) )
      .withColumn( "stddevZ", pow($"varianceZ",0.50) )
dataFeatDF: org.apache.spark.sql.DataFrame = [user_id: string, activity: string ... 27 more fields]
display(dataFeatDF.sample(false,0.1))
user_id activity timeStampAsLong x y z meanX meanY meanZ SqX SqY SqZ resultant meanResultant absDevFromMeanX absDevFromMeanY absDevFromMeanZ meanAbsDevFromMeanX meanAbsDevFromMeanY meanAbsDevFromMeanZ sqrDevFromMeanX sqrDevFromMeanY sqrDevFromMeanZ varianceX varianceY varianceZ stddevX stddevY stddevZ
user_001 Jogging 1.446047140892e12 -5.01936 0.383802 -1.61005 3.0104863636363643 -8.294006090909091 0.4139589090909091 25.193974809599997 0.147303975204 2.5922610025 5.285218991423534 12.114445037568451 8.029846363636365 8.67780809090909 2.024008909090909 5.574814628099175 8.743996363636365 1.8780127768595039 64.47843262360415 75.30435326264728 4.0966120640793715 39.26105423020038 86.44128603240851 4.762676135262259 6.265864204577081 9.297380600599746 2.1823556390428807
user_001 Jogging 1.446047141346e12 0.498763 -7.51018 1.83878 2.8084320909090907 -6.935377181818183 -4.936863636363633e-2 0.24876453016900002 56.4028036324 3.3811118884000004 7.748075893469875 10.526229014345958 2.309669090909091 0.5748028181818174 1.8881486363636364 4.870479504132231 7.062020214876034 2.769514024793388 5.334571309500826 0.3303982797897595 3.5651052730018598 28.32052218489271 67.50085446063852 9.63958031560342 5.3217029403089295 8.215890363231397 3.104767352895128
user_001 Jogging 1.44604714141e12 11.87989 -19.58108 2.75846 3.738570272727273 -7.440509 -7.027136363636353e-2 141.13178641209998 383.4186939664 7.609101571599999 23.06858430745372 11.31119913133375 8.141319727272727 12.140571000000001 2.8287313636363636 5.357875181818181 7.761603768595041 2.783764652892562 66.28108690168007 147.39346420604105 8.00172112762004 33.64351026346047 79.10395343437911 9.717968828501292 5.800302601025266 8.894040332401191 3.1173656873233995
user_001 Jogging 1.446047142255e12 5.32712 -18.35483 3.94639 3.254341727272727 -8.088470909090908 0.69265 28.378207494399998 336.8997843289 15.5739940321 19.515429430463477 14.672311468733064 2.0727782727272728 10.266359090909091 3.25374 4.968022991735537 9.121183421487604 2.997534545454546 4.296409767890256 105.39812898349174 10.5868239876 42.373279917383705 108.65275154076608 11.80757071836034 6.509476163055189 10.423663057714695 3.4362145914305673
user_001 Jogging 1.44604714236e12 -3.90807 1.87829 -1.03525 -0.38260427272727265 -4.622226636363637 1.309258636363637 15.2730111249 3.5279733241 1.0717425625 4.457883692011267 6.235267429173871 3.5254657272727274 6.500516636363637 2.3445086363636367 2.0246421404958674 4.5952694710743796 1.275971702479339 12.42890859417462 42.25671653964041 5.496720745983679 5.322841770497276 27.27538573170004 2.7565803183488558 2.3071284685724107 5.222584200537129 1.660295250354242
user_001 Jogging 1.446047142611e12 3.14286 -19.58108 11.57214 4.797603636363636 -11.600005181818183 3.4970007272727273 9.877568979600001 383.4186939664 133.9144241796 22.961068945621847 17.859074479791374 1.6547436363636359 7.981074818181817 8.075139272727272 4.461625685950413 7.032252909090909 8.588184256198346 2.7381765020859485 63.69755525341592 65.20787427394234 29.39875554713526 63.52664671148329 111.91945306916881 5.422061927637424 7.970360513269352 10.579199075032514
user_001 Jogging 1.446047142723e12 3.33447 -16.4005 4.59784 8.695826363636364 -19.19787727272727 1.5635675454545455 11.1186901809 268.97640025000004 21.140132665599996 17.356129265953857 21.88260842177062 5.361356363636364 2.7973772727272674 3.0342724545454542 5.770848892561983 0.974475619834712 4.766286942148761 28.74414205790414 7.825319605971044 9.206809328413296 47.590515226108074 2.4736297184957947 29.04037921776094 6.898587915371382 1.5727777079090977 5.3889126192359935
user_001 Jogging 1.446047143007e12 13.94919 -19.58108 -1.99325 7.406869090909091 -15.54699727272727 -2.132600909090909 194.5799016561 383.4186939664 3.9730455625 24.124088401118915 17.659646578855703 6.5423209090909085 4.034082727272731 0.13935090909090886 4.869846033057851 6.8751705371900815 2.2795826446280993 42.80196287752809 16.273823450480194 1.9418675864462744e-2 25.026920417585174 50.28981774904209 8.028885422595941 5.002691317439561 7.091531410706865 2.8335287933239606
user_001 Jogging 1.446047143412e12 -3.7722e-2 -19.38948 16.74538 2.933844363636364 -10.001001818181818 4.7859561818181815 1.422949284e-3 375.95193467039996 280.4077513444 25.61954544803799 14.94696596077227 2.971566363636364 9.388478181818181 11.959423818181818 4.184833462809917 6.708588429752067 8.137841272727274 8.830206653495043 88.14352257047602 143.0278180628946 25.580893194814248 48.75439847000317 93.00363187197318 5.057755746851981 6.9824349957592275 9.643839062944444
user_001 Jogging 1.446047143428e12 5.99e-4 -19.58108 2.49022 2.0455097272727274 -12.96560090909091 4.8382107272727275 3.5880100000000004e-7 383.4186939664 6.2011956484 19.738791502359028 17.17647355875381 2.0449107272727276 6.615479090909091 2.3479907272727276 3.7078880247933883 7.136446049586777 7.307778793388429 4.181659882515076 43.764563602255365 5.513060455358713 22.443816935824188 54.075963421190316 85.24184299019907 4.737490573692384 7.3536360680407835 9.232650918896429
user_001 Jogging 1.4460471435e12 8.92923 -19.58108 7.62514 0.5335997272727272 -19.581079999999996 1.8318090909090905 79.73114839290001 383.4186939664 58.1427600196 22.831833092831157 21.106302639228264 8.395630272727272 3.552713678800501e-15 5.793330909090909 4.901198421487603 2.9142437190082675 3.942557785123967 70.48660767633461 1.2621774483536189e-29 33.5626830222281 33.313236846605356 15.557764988992716 30.291063062675242 5.771762022693361 3.944333275598389 5.503731739708544
user_001 Jogging 1.446047143517e12 10.42372 -19.58108 8.73643 2.205758909090909 -19.581079999999996 2.4379672727272723 108.65393863839999 383.4186939664 76.3252091449 23.841095649103462 21.67139468669904 8.21796109090909 3.552713678800501e-15 6.298462727272728 6.114780479338842 1.5831671074380202 4.6259896033057855 67.53488449169573 1.2621774483536189e-29 39.67063272684381 45.04989788390212 5.722576186684003 36.09638973021352 6.711922070756045 2.3921906668750306 6.008027107979251
user_001 Jogging 1.446047143581e12 14.17911 -4.75112 -8.58435 12.837903636363638 -14.822395454545456 1.539181818181818 201.04716039209998 22.573141254400003 73.6910649225 17.24271923360698 21.99929601707681 1.3412063636363616 10.071275454545455 10.123531818181819 6.092612942148761 3.6242771074380187 7.671663884297521 1.7988345098586722 101.43058928132977 102.48589647373969 41.440687896949285 28.9054852091499 72.55417043068063 6.437444205346504 5.376382167326827 8.517873586211563
user_001 Jogging 1.446047143606e12 9.23579 -0.497565 0.919089 13.25594272727273 -10.042807727272727 -1.2721355454545458 85.2998169241 0.24757092922499999 0.8447245899210001 9.294735738214724 18.876966595567662 4.02015272727273 9.545242727272727 2.1912245454545456 4.424255107438015 6.262994958677688 6.90810826446281 16.161627950598373 91.11165872255289 4.80146500860248 24.680606942273855 54.43818419281497 66.47172910922194 4.967958025413847 7.378223647519434 8.153019631352665
user_001 Jogging 1.44604714363e12 5.82529 3.14286 3.21831 11.935633636363635 -4.315663545454545 -2.742242818181819 33.9340035841 9.877568979600001 10.357519256099998 7.359965476807618 14.48403310791005 6.110343636363635 7.458523545454545 5.960552818181819 4.2234690247933875 8.366494983471073 7.1579815123966934 37.33629935444957 55.629573478099836 35.52818989833523 22.091004368014264 72.82379547301899 68.08732499721447 4.700106846446607 8.53368592537943 8.251504408119436
user_001 Jogging 1.446047143687e12 0.805325 5.40376 -1.18853 4.815022272727273 3.9789428181818183 1.4346706363636363 0.6485483556249999 29.2006221376 1.4126035609000003 5.591222947989554 7.279610887559767 4.009697272727273 1.4248171818181818 2.623200636363636 4.808407685950414 5.901961702479338 3.262293380165289 16.07767221891653 2.0301040016043057 6.881181578618586 23.86087788087626 40.88601350062889 14.184341683283828 4.8847597567205145 6.394217192168944 3.7662105203086864
user_001 Jogging 1.446047143703e12 0.498763 3.67935 -5.0972 3.3832365454545457 4.700061818181818 0.36518618181818213 0.24876453016900002 13.5376164225 25.98144784 6.306173863181145 6.765815236942559 2.884473545454546 1.0207118181818182 5.462386181818182 4.530347388429752 4.320377892561984 3.515650859504132 8.320187634427118 1.041852615776033 29.83766279931822 21.64134645781683 25.2878319216034 16.07774203478182 4.652026059451606 5.028700818462299 4.009705978595166
user_001 Jogging 1.4460471438e12 6.36177 -19.58108 6.55217 2.181372181818182 -11.164546363636363 3.423636363636378e-2 40.4721175329 383.4186939664 42.930931708900005 21.60605802103197 12.990120579315441 4.180397818181818 8.416533636363637 6.517933636363637 2.872756842975207 9.207959504132232 3.702816834710744 17.475725918259307 70.83803845204051 42.4834588880405 10.08973643029246 92.24096030173884 21.23336541278622 3.1764345468295834 9.604215756725733 4.607967601099884
user_001 Jogging 1.446047143865e12 7.66466 -19.58108 2.37526 6.337383636363636 -19.581079999999996 3.5875754545454543 58.747012915599996 383.4186939664 5.6418600676 21.1614641967327 21.061833583938864 1.3272763636363631 3.552713678800501e-15 1.2123154545454544 2.492719975206612 4.63169049586777 2.403411570247934 1.7616625454677672 1.2621774483536189e-29 1.4697087613297517 7.974185257215893 38.68784266457513 9.625501871091812 2.82385999249536 6.21995519795562 3.1024992942935237
user_001 Jogging 1.446047143906e12 2.22318 -17.58843 3.67815 5.58143 -19.372060909090905 3.406424545454546 4.9425293124000005 309.35286986489996 13.5287874225 18.10591579014439 20.5777606506816 3.35825 1.7836309090909062 0.27172545454545416 1.7852188099173552 0.911135950413226 1.229100991735537 11.2778430625 3.1813392198644523 7.383472264793367e-2 4.562496695217112 2.185291967910373 2.2448866682423736 2.136000162738082 1.4782733062293905 1.4982945866025057
user_001 Jogging 1.446047143914e12 2.03158 -15.25089 2.91174 5.28531909090909 -18.97840727272727 3.3541690909090907 4.127317296399999 232.58964579210001 8.4782298276 15.658709810073754 20.13034914244241 3.2537390909090904 3.7275172727272707 0.44242909090909066 1.9736531404958675 0.9219033057851264 1.1711456198347105 10.586818071709914 13.89438501848015 0.1957435004826444 5.398146523816002 2.2642876788123227 2.1566573067818178 2.32339116892012 1.5047550228566517 1.468556198033231
user_001 Jogging 1.446047143946e12 0.805325 -4.67448 1.80046 3.285695 -15.020963636363634 2.7131754545454543 0.6485483556249999 21.850763270399998 3.2416562115999996 5.073555739087233 15.738688413790378 2.48037 10.346483636363633 0.9127154545454543 2.33848826446281 3.4744802479338843 0.8097950413223138 6.152235336900001 107.04972363754042 0.8330495009661153 7.003361392995342 26.536731773096072 0.9551943565163034 2.6463864783880946 5.15138154023715 0.9773404506702377
user_001 Jogging 1.446047144043e12 -4.78944 6.93658 0.114362 -4.071804181818182 5.051913545454545 -2.2614949999999996 22.938735513599998 48.116142096400004 1.3078667044000002e-2 8.430181271897064 7.023773744750437 0.7176358181818179 1.8846664545454548 2.3758569999999994 2.8974588016528924 7.285610578512396 2.8448858760330578 0.5150011675374871 3.5519676448889346 5.644696484448997 9.729573142987029 65.17831055224397 9.956481900398632 3.119226369308106 8.073308525768352 3.1553893421254107
user_001 Jogging 1.446047144092e12 -1.99206 4.21583 -2.98958 -4.1693490909090904 6.340868181818181 -2.1778882727272726 3.9683030435999997 17.773222588900005 8.937588576400001 5.538873008916164 8.085371578268587 2.1772890909090905 2.125038181818181 0.8116917272727275 1.5590985867768594 2.253931280991736 1.5172942727272727 4.7405877853917335 4.51578727418512 0.6588434601229839 3.3676530779136438 8.457330240795045 3.1033527599789106 1.8351166387763052 2.9081489371755094 1.761633548720877
user_001 Jogging 1.446047144115e12 3.60271 3.8919e-2 -6.36177 -2.4414504545454547 4.870761454545455 -2.3311700909090907 12.9795193441 1.514688561e-3 40.4721175329 7.3111662247250955 6.858484763711422 6.044160454545455 4.8318424545454555 4.03059990909091 1.9356506115702479 2.061379578512397 1.4881586776859501 36.53187560029112 23.346701505547852 16.24573562716365 6.431645076172794 6.610973877450948 3.3286675864357367 2.536068823232681 2.5711814166742393 1.824463643495188
user_001 Jogging 1.44604714414e12 6.28513 -1.72382 3.60151 0.6938477272727271 3.0348691818181806 -2.150019636363636 39.5028591169 2.9715553923999996 12.970874280100002 7.446159331454035 6.6932802788723516 5.591282272727272 4.7586891818181805 5.751529636363636 3.6945847933884295 2.4996878512396696 2.011975041322314 31.262437453314252 22.645122729153385 33.08009315796922 20.548499768802852 9.118378197963445 7.077055657840811 4.533045308487756 3.0196652460104656 2.6602736058234333
user_001 Jogging 1.44604714418e12 -3.56319 -9.92436 -3.98591 2.9617137272727274 -2.009475363636364 0.6369127272727273 12.696322976100001 98.4929214096 15.8874785281 11.272831184480676 7.331966995972979 6.5249037272727275 7.914884636363636 4.622822727272728 4.575635462809917 4.63612326446281 4.079687826446281 42.57436865017753 62.64539880694513 21.370489967789258 26.438045152664895 23.685324490452658 22.525681280821853 5.141793962486721 4.866757081512561 4.74612276293206
user_001 Jogging 1.446047144221e12 4.714 -19.58108 7.6042e-2 3.884886 -8.196463636363637 3.967295636363637 22.221796000000005 383.4186939664 5.782385764e-3 20.140662162703688 14.018026468325372 0.8291140000000006 11.384616363636363 3.8912536363636367 3.830131181818182 6.218974305785125 8.42825211570248 0.6874300249960009 129.60948974717684 15.141854862513226 19.765861701657393 44.709337568159334 94.92463205415766 4.445881431353899 6.686504136554418 9.742927283632865
user_001 Jogging 1.446047144254e12 -1.18733 -19.58108 7.93171 2.818885454545455 -14.29636090909091 4.907885636363637 1.4097525289 383.4186939664 62.9120235241 21.159878780829533 19.09860199176969 4.006215454545455 5.284719090909091 3.023824363636363 3.438377512396694 7.292894024793389 7.597556247933884 16.049762268238844 27.928255869819008 9.143513782120856 17.21997488706634 58.23402061541601 88.07572005384371 4.1496957583739 7.6311218451428235 9.38486654427455
user_001 Jogging 1.446047144278e12 1.22685 -19.58108 5.44089 3.083644 -17.351535454545452 8.287040181818181 1.5051609225 383.4186939664 29.603283992099996 20.35993955985626 20.824887979127013 1.856794 2.229544545454548 2.8461501818181816 3.1305487933884297 6.410893917355373 5.5722790413223136 3.4476839584360004 4.970868880166127 8.100570857463667 14.594451388452198 49.33036109995855 50.57366699564773 3.8202684969059697 7.023557581451052 7.111516504631606
user_001 Jogging 1.446047144311e12 11.49669 -19.58108 7.39522 4.355181272727273 -19.535792727272725 6.182906363636363 132.1738809561 383.4186939664 54.6892788484 23.880574820780595 21.77720408013568 7.1415087272727265 4.528727272727551e-2 1.2123136363636373 4.527814231404959 3.726571074380167 2.767612314049586 51.00114690171252 2.050937071074632e-3 1.4697043529132254 29.305284421350223 23.940853207647194 8.62882105866129 5.413435546984024 4.892939117508739 2.937485499310812
user_001 Jogging 1.446047144521e12 2.95126 -1.11069 -7.47306 2.6133480000000002 2.1569868181818177 -3.048805 8.7099355876 1.2336322760999998 55.8466257636 8.111115436689333 5.523819861858547 0.33791199999999977 3.2676768181818177 4.4242550000000005 3.396256438016529 3.6597486033057858 3.397523859504133 0.11418451974399985 10.677711788082847 19.574032305025003 16.3348600923496 20.826787642321772 14.775003279205595 4.041640767355457 4.5636375450206135 3.8438266453113616
user_001 Jogging 1.44604714465e12 1.99325 -19.58108 4.25296 3.5539354545454547 -19.33373999999999 3.173021363636363 3.9730455625 383.4186939664 18.0876687616 20.136519269488954 20.04234972512039 1.5606854545454547 0.24734000000000833 1.0799386363636367 1.341211223140496 5.445601107438019 1.5103279338842974 2.4357390880297527 6.117707560000412e-2 1.1662674583109511 2.0902997020591165 46.50264074581899 3.8864219929065356 1.4457868798889817 6.819284474621878 1.9714010228531726
user_001 Jogging 1.446047144779e12 -0.191003 0.920286 -0.230521 2.95823 -5.57326509090909 0.24325772727272724 3.6482146009e-2 0.8469263217960001 5.3139931441e-2 0.9677543072732873 6.782599679498083 3.1492329999999997 6.49355109090909 0.47377872727272724 1.9058816776859502 7.382202495867769 1.6845096694214876 9.917668488288998 42.166205770246634 0.22446628241616526 4.348254975048362 56.287978164098156 4.396775017887605 2.0852469817861774 7.502531450390472 2.096848830480539
user_001 Jogging 1.446047144909e12 3.44943 2.8363 -4.59904 -1.8422599999999998 5.741678181818181 -3.3414341818181814 11.8985673249 8.04459769 21.151168921599997 6.410486248054823 8.646625001195995 5.29169 2.905378181818181 1.2576058181818182 1.700345950413223 2.538641636363636 4.040733280991735 28.0019830561 8.44122237938512 1.5815723939247603 5.881941722491503 7.297593555367826 31.585934417060354 2.4252714739780172 2.7014058479554355 5.620136512315368
user_001 Jogging 1.446047144965e12 -1.49389 -10.80573 -8.50771 1.8608763636363634 -1.807423636363636 -0.2583900000000001 2.2317073320999996 116.76380083290002 72.3811294441 13.833894520672768 10.624124936163746 3.3547663636363634 8.998306363636365 8.249319999999999 3.971061611570248 5.76831652892562 7.454093057851239 11.254457354585949 80.9695174138587 68.05128046239999 21.70051268411826 45.90407271894876 64.16546233071315 4.658380908010664 6.775254439425043 8.010334720266885
user_001 Jogging 1.446047145006e12 5.2888 -19.50444 1.26397 4.592069272727273 -9.882558181818181 4.744153636363636 27.97140544 380.42317971359995 1.5976201609 20.248264254362642 15.73332539025025 0.696730727272727 9.621881818181818 3.4801836363636363 3.560938619834711 8.04219826446281 9.370108743801651 0.4854337063259831 92.58060972305783 12.111678142813222 18.604081060610227 68.5146688204746 105.59536052408288 4.3132448412546935 8.277358807039514 10.275960321258685
user_001 Jogging 1.446047145063e12 3.83263 -19.58108 6.51385 2.3694895454545457 -17.786991818181818 6.966730909090909 14.6890527169 383.4186939664 42.430241822499994 20.988996843722663 20.711596889168277 1.4631404545454543 1.7940881818181822 0.4528809090909096 3.6613319669421487 5.671721735537191 3.724989256198347 2.1407799897274784 3.218752404139671 0.20510111781900875 18.391050523378283 38.52759670800473 38.85600186927499 4.288478812280443 6.207060230737634 6.233458259206922
user_001 Jogging 1.446047145095e12 8.39275 -19.58108 7.77842 3.1184786363636365 -19.581079999999996 5.907696363636364 70.4382525625 383.4186939664 60.50381769639999 22.679523015824206 21.447303073035563 5.2742713636363625 3.552713678800501e-15 1.8707236363636355 5.020279380165289 3.0450398347107455 1.37161479338843 27.817938417274576 1.2621774483536189e-29 3.4996069236495835 31.002898462194388 16.330388050525777 2.60981791889955 5.568024646335035 4.041087483651619 1.6154930884716128
user_001 Jogging 1.446047145298e12 2.4531 2.68302 -2.18486 2.9512618181818184 2.784047636363636 -1.7006264545454548 6.01769961 7.1985963204 4.7736132196000005 4.241451302325656 4.838002482542072 0.49816181818181837 0.10102763636363621 0.4842335454545452 2.036044016528926 4.023950479338843 1.7253638842975207 0.24816519709421506 1.0206583309223109e-2 0.2344821265434791 5.415028704769436 23.42669537789521 4.255417333194267 2.3270214233585036 4.84011315755068 2.062866290672827
user_001 Jogging 1.446047145826e12 3.18118 -19.58108 4.7128 5.462984545454545 -11.24467181818182 3.880204545454545 10.1199061924 383.4186939664 22.21048384 20.389926042013983 16.88118003999633 2.2818045454545453 8.33640818181818 0.8325954545454546 3.494114983471074 8.170460165289256 7.975376504132232 5.206631983657024 69.4957013738851 0.6932151909297521 16.238127510167725 74.18152678299337 85.41361229590531 4.0296560039496825 8.612869834323131 9.241948511861843
user_001 Jogging 1.446047145906e12 7.24314 -19.58108 1.57053 1.3661963636363637 -19.581079999999996 4.9705900000000005 52.4630770596 383.4186939664 2.4665644809 20.936769939675507 20.824778135048515 5.876943636363636 3.552713678800501e-15 3.4000600000000007 4.809673801652893 3.080192148760331 2.9028430578512396 34.53846650499504 1.2621774483536189e-29 11.560408003600005 26.078049228796736 17.058755092359807 9.280744192829529 5.10666713510845 4.130224581346614 3.0464313865290857
user_001 Jogging 1.446047145914e12 4.79064 -19.58108 2.52854 1.5125109090909092 -19.581079999999996 4.772020909090909 22.9502316096 383.4186939664 6.3935145316 20.316555813119503 20.818108114239923 3.2781290909090908 3.552713678800501e-15 2.2434809090909087 4.9002487603305775 2.3223368595041345 3.0311053719008267 10.746130336664462 1.2621774483536189e-29 5.03320658945537 26.581639988161047 10.74096405837025 9.675288865422766 5.155738549244041 3.277341004285372 3.1105126370781337
user_001 Jogging 1.446047145947e12 2.68302 -16.24721 0.267643 3.2264732727272727 -19.002790909090912 2.504155 7.1985963204 263.97183278409995 7.163277544900001e-2 16.46942809814442 19.77419717829964 0.5434532727272727 2.755580909090913 2.236512 2.9690325619834708 0.9991787603305805 2.7372102479338847 0.29534145963798347 7.593226146546302 5.001985926143999 13.834117142120611 2.145853908953498 7.944784113633844 3.719424302512502 1.4648733422905538 2.8186493420845813
user_001 Jogging 1.446047146142e12 2.49142 -2.22198 -3.41111 6.225908181818181 3.0348706363636366 -3.9092709090909086 6.207173616400001 4.937195120399999 11.635671432099999 4.772844033582074 8.453049060126027 3.734488181818181 5.2568506363636365 0.4981609090909087 2.676405371900827 3.922289024793389 1.6018522727272726 13.946401980139665 27.63447861303677 0.24816429134628062 8.224617051718033 20.548089963168977 5.414473050834811 2.867859315189299 4.533000106239683 2.3269020286283673
user_001 Jogging 1.446047146191e12 2.2615 -18.23987 1.8771 3.0209363636363644 -5.601133909090908 -1.3069736363636362 5.114382249999999 332.69285761689997 3.52350441 18.475138545540055 8.593185614974145 0.7594363636363646 12.638736090909092 3.184073636363636 2.3581242148760326 6.585709553719008 2.062647512396694 0.5767435904132245 159.73764997564803 10.13832492178595 6.783338460343121 54.960802016525165 6.4349872719740056 2.6044842983483547 7.413555288559273 2.5367276700454084
user_001 Jogging 1.446047146222e12 6.70665 -19.58108 1.34061 3.292661818181818 -13.000438181818181 0.8041272727272727 44.9791542225 383.4186939664 1.7972351721000002 20.741144697460648 13.747680096855284 3.4139881818181816 6.580641818181819 0.5364827272727274 1.9527515702479334 8.756033107438014 2.4198804049586773 11.655315305594213 43.30484673920332 0.2878137166619836 5.276590136867767 83.31892515202385 7.355384939688656 2.2970829625565914 9.127920089046784 2.7120812929719964
user_001 Jogging 1.446047146247e12 6.70665 -19.58108 -2.0699 4.581617272727272 -17.348051818181816 1.1106894545454544 44.9791542225 383.4186939664 4.28448601 20.801017624118778 18.08485443258767 2.1250327272727274 2.2330281818181845 3.1805894545454545 1.8029535537190085 8.180911776859503 2.438882479338843 4.515764091980166 4.986414860794227 10.116149278365752 4.334497354961382 78.27161570846312 7.517023131813722 2.081945569644265 8.847124714191787 2.7417190103680795
user_001 Jogging 1.446047146255e12 6.55337 -19.58108 -1.61005 4.947401818181818 -18.389667272727266 0.8738004545454544 42.9466583569 383.4186939664 2.5922610025 20.71129192797494 19.18895665104643 1.6059681818181826 1.1914127272727342 2.4838504545454545 1.8089707438016531 7.583304611570248 2.3552742644628095 2.579133801012399 1.4194642867074545 6.169513080545661 4.353425914253344 72.91914457913747 7.02478885722426 2.086486499897218 8.539270728764691 2.6504318246701346
user_001 Jogging 1.446047146271e12 5.74865 -19.58108 -0.307161 5.564010909090908 -19.452184545454543 0.41047318181818165 33.04697682249999 383.4186939664 9.434787992100001e-2 20.409802024243668 20.332815201913306 0.18463909090909159 0.12889545454545726 0.7176341818181817 1.7611500826446287 5.651453752066117 1.715229809917355 3.4091593891735786e-2 1.6614038202480037e-2 0.5149988189138511 4.313352366296018 51.02793158470397 3.854774185943344 2.076861181277174 7.143383762944839 1.9633578853442244
user_001 Jogging 1.446047146295e12 4.10087 -19.58108 -0.422122 5.940246363636363 -19.581079999999996 -7.566363636363579e-3 16.817134756899996 383.4186939664 0.178186982884 20.010347715774056 20.51464954273569 1.8393763636363634 3.552713678800501e-15 0.4145556363636364 1.8916290082644627 2.4962036611570273 1.1429585702479337 3.3833054071041313 1.2621774483536189e-29 0.17185637564085954 4.597386198170472 14.204368818450723 2.222369381335169 2.1441516266743994 3.7688683737231687 1.490761342849743
user_001 Jogging 1.44604714649e12 0.958607 3.52607 0.344284 -0.678715818181818 1.8713269090909093 2.333455818181818 0.918927380449 12.4331696449 0.11853147265599999 3.6702354826366386 3.7110363855085042 1.637322818181818 1.6547430909090906 1.989171818181818 1.7076289090909091 3.528951776859505 1.723146338842975 2.680826010938851 2.7381746969113707 3.95680452224876 3.4146557666225394 14.091008592012436 3.72855255493712 1.847878720755921 3.753799221057572 1.9309460258995124
user_001 Jogging 1.446047146627e12 8.77595 -15.13592 11.64878 3.8744349090909096 -4.806858181818182 -2.1465371818181818 77.0172984025 229.0960742464 135.69407548840002 21.01921616372266 10.213391746577853 4.90151509090909 10.329061818181819 13.795317181818183 3.0817764958677687 5.029777553719009 5.655888396694215 24.024850186409545 106.6895180438215 190.31077614696795 12.519304124182344 31.099654858346547 56.03006032522963 3.538262868157529 5.576706452588889 7.485322994048395
user_001 Jogging 1.4460471467e12 0.881966 -19.58108 -1.45677 3.3065973636363637 -18.302574545454544 6.210776818181818 0.7778640251560001 383.4186939664 2.1221788328999995 19.654992669152943 20.497246490507834 2.4246313636363634 1.2785054545454564 7.667546818181818 3.0073537190082646 6.956878148760333 7.472461669421488 5.8788372495291314 1.6345761973024842 58.79127420901012 11.837209034079082 60.051072653539926 68.10106476024005 3.440524528916933 7.7492627167711845 8.252336927212804
user_001 Jogging 1.446047146708e12 2.18486 -19.58108 -0.1922 2.616831909090909 -19.065497272727267 5.611586818181818 4.7736132196000005 383.4186939664 3.694084e-2 19.703533896892708 20.818008869068755 0.4319719090909091 0.5155827272727329 5.803786818181818 2.473402603305785 6.281047404958678 7.099076429752066 0.18659973024364462 0.26582554866198926 33.68394143090103 8.239763534897493 54.32996020046944 62.23338618681305 2.8704988303250523 7.370885984769364 7.888813991140433
user_001 Jogging 1.446047146789e12 5.94025 -12.68342 0.804128 5.170359090909091 -17.612809090909092 2.316038 35.2865700625 160.8691428964 0.646621840384 14.02862554918635 18.616420879792923 0.7698909090909085 4.929389090909092 1.5119099999999999 2.1500545950413223 1.5967857024793408 1.880862933884297 0.5927320119008256 24.298876809573567 2.2858718480999998 5.820509118572988 5.918452160384152 5.775440422698065 2.4125731322745407 2.4327869122436825 2.4032146018818348
user_001 Jogging 1.446047146846e12 14.94552 2.52974 -7.08986 8.124505454545455 -8.865327727272726 -0.9760245454545455 223.36856807040002 6.3995844675999995 50.2661148196 16.734224432509563 14.08539729512732 6.821014545454545 11.395067727272727 6.1138354545454545 2.543391082644628 6.365605413223141 2.754627909090909 46.52623942930248 129.84756850913243 37.37898396525703 11.835538075822928 47.25518283891866 14.352842783440092 3.4402816855343294 6.874240528154267 3.7885145879935704
user_001 Jogging 1.44604714691e12 2.6447 6.51505 -2.14654 8.817753636363635 3.034871363636364 -3.5852909090909093 6.994438089999999 42.44587650249999 4.607633971599999 7.351730991004771 10.905216461572586 6.173053636363635 3.4801786363636356 1.4387509090909094 4.208898595041322 7.25900756198347 2.4344469173553724 38.1065911974223 12.111643341001853 2.0700041784099183 22.049739906490682 58.57205085462563 13.497022673672406 4.69571505805992 7.653237932707021 3.673829429038916
user_001 Jogging 1.446047146926e12 0.881966 6.09353 -1.80165 6.790261454545456 4.644324545454546 -2.839787272727272 0.7778640251560001 37.1311078609 3.2459427224999997 6.4152096309127735 9.492024266035791 5.908295454545455 1.4492054545454547 1.0381372727272722 4.2548196694214875 5.969101487603305 1.4526874958677687 34.90795517820249 2.1001964494842977 1.0777289970256188 22.276377763682646 44.06520485639808 4.615243289794645 4.719785775189658 6.63816276212011 2.1483117301254593
user_001 Jogging 1.446047146991e12 5.71033 -7.7401 3.67815 1.2895554545454546 1.2895539999999999 0.4069892727272728 32.6078687089 59.90914801 13.5287874225 10.29785434648403 5.452298577041354 4.420774545454545 9.029654 3.2711607272727274 4.018882578512398 4.053401785123968 2.1415043057851237 19.543247581738843 81.53465135971601 10.70049250365144 19.656272774198364 24.692266006893522 5.525528248539532 4.433539531141948 4.969131313106298 2.3506442198979265
user_001 Jogging 1.446047147008e12 5.86361 -14.5228 1.64717 1.996739090909091 -2.2498487272727274 1.2430692727272727 34.3819222321 210.91171984000002 2.7131690089 15.748231998576857 6.790361057403035 3.8668709090909097 12.272951272727273 0.4041007272727273 3.7151708429752066 5.61915094214876 2.1373874958677685 14.952690627573558 150.62533294273797 0.16329739778234711 16.52413057886283 47.64363520050973 5.706252704011319 4.064988386067398 6.902436903044441 2.3887764031008256
user_001 Jogging 1.44604714755e12 16.86154 -19.58108 -1.49509 6.253777272727273 -19.581079999999996 3.8035627272727273 284.31153117160005 383.4186939664 2.2352941081 25.883692148650276 21.360767742613746 10.607762727272728 3.552713678800501e-15 5.298652727272727 3.1489165289256196 3.1394150413223163 2.8486857355371904 112.52463007811656 1.2621774483536189e-29 28.07572072423471 16.449431349785637 18.39730278650308 10.253797064157284 4.055789855229883 4.289207710813628 3.2021550656014903
user_001 Jogging 1.446047147622e12 2.37646 -6.36057 -5.13552 6.630013181818182 -14.672596363636364 0.23280781818181825 5.647562131599999 40.4568507249 26.373565670399998 8.513399939325064 17.26086851800695 4.253553181818182 8.312026363636363 5.368327818181818 5.596982917355372 3.5789906611570257 3.841849239669422 18.09271467055558 69.08978226978594 28.81894356346476 38.34505562899607 23.791265035335616 19.437297262372166 6.192338462083292 4.877629038306995 4.408775029684795
user_001 Jogging 1.446047147639e12 2.10822 -3.86975 -4.36911 4.651291363636364 -11.934435454545456 -0.6485594545454547 4.444591568400001 14.974965062499999 19.0891221921 6.205536143074182 14.146659379883403 2.543071363636364 8.064685454545456 3.7205505454545453 4.807773413223141 5.056698264462809 3.875102727272727 6.467211960547316 65.03915148075706 13.842496361282114 28.276395911400765 35.80188864520639 19.261341575418438 5.317555445070673 5.983467944696152 4.388774495849432
user_001 Jogging 1.446047147655e12 3.2195 -0.995729 -4.86728 2.839785 -8.691143545454544 -1.735463090909091 10.36518025 0.991476241441 23.6904145984 5.920056679613887 10.914676311816635 0.379715 7.695414545454544 3.131816909090909 3.883018702479339 6.473599669421486 4.033451586776859 0.14418348122500002 59.21940502639337 9.808277152067735 21.574299434066237 46.895448857992044 19.698109391720433 4.644814251836799 6.848025179421586 4.438255219308646
user_001 Jogging 1.446047148035e12 -2.52854 0.307161 1.80046 2.7596614545454545 -7.064272636363637 0.633429 6.3935145316 9.434787992100001e-2 3.2416562115999996 3.1192176299708554 8.707368733999472 5.2882014545454545 7.371433636363637 1.167031 4.633590611570247 7.0259181818181835 0.9637088925619838 27.965074623856662 54.338033855313235 1.361961354961 26.853786031159323 51.463071213056516 1.4078366659209935 5.1820638775645484 7.1737766352916585 1.1865229310556933
user_001 Jogging 1.446047148423e12 3.41111 -10.84405 -5.99e-4 4.522395454545454 -16.672220000000003 2.9640000909090904 11.635671432099999 117.59342040249999 3.5880100000000004e-7 11.367897439430081 17.70845344887635 1.1112854545454542 5.828170000000004 2.9645990909090902 2.8486870247933878 2.1940752892561997 1.3709815702479338 1.2349553614842967 33.96756554890004 8.788847769819004 9.0019158055592 10.105985401013 2.663159615259104 3.0003192839361614 3.1789912552589694 1.6319189977627884
user_001 Jogging 1.446047148585e12 3.10454 -5.24928 -0.230521 7.291908181818181 -0.17706772727272738 -1.0526655454545453 9.638168611600001 27.5549405184 5.3139931441e-2 6.102970511270803 8.810267540587791 4.187368181818181 5.072212272727272 0.8221445454545453 2.3407064462809912 2.738793338842975 5.057014528925619 17.5340522901033 25.72733733960516 0.6759216536206609 8.01479266604553 10.180405784232084 31.71471424852974 2.8310409156431366 3.1906748164349317 5.631581860235163
user_001 Jogging 1.446047148658e12 8.85259 -19.58108 -0.996927 5.82877 -13.097980909090909 3.5980274545454547 78.36834970809998 383.4186939664 0.993863443329 21.512343134066754 15.243843861466813 3.0238199999999997 6.483099090909091 4.594954454545455 1.8757956198347103 7.861681504132232 4.55061688429752 9.143487392399999 42.03057382254628 21.11360643934712 5.88666845142667 68.0709621098762 23.399370359750957 2.426245752479882 8.250512839204372 4.837289567490348
user_001 Jogging 1.446047148723e12 11.57333 -19.58108 4.5212 11.754482727272727 -19.581079999999996 3.4377791818181818 133.9419672889 383.4186939664 20.441249440000004 23.19055649818046 23.48316918410363 0.18115272727272647 3.552713678800501e-15 1.0834208181818186 3.3810542975206612 3.4684628016528944 2.8087840661157024 3.281631059834682e-2 1.2621774483536189e-29 1.1738006692697611 15.367657156510823 23.07182841418071 12.982727905804962 3.9201603483162297 4.803314315572187 3.603155270843176
user_001 Jogging 1.446047148933e12 -6.55217 0.958607 0.305964 -8.673726363636364 1.5926342727272726 -1.1432400909090907 42.930931708900005 0.918927380449 9.361396929600001e-2 6.628987332816756 10.970671818551988 2.1215563636363637 0.6340272727272727 1.4492040909090909 6.460932644628099 4.056886380165289 2.3039676280991737 4.501001404085951 0.4019905825619834 2.1001924971076447 69.60176164731864 24.599329097919824 6.676603281846297 8.342767025832535 4.959771073136322 2.5839123982531405
user_001 Jogging 1.446047148956e12 0.805325 0.996927 -7.81794 -5.966918636363638 1.8991967272727273 -2.0733782727272723 0.6485483556249999 0.993863443329 61.120185843600005 7.92228487511993 9.345324426929823 6.772243636363638 0.9022697272727273 5.744561727272728 4.943003884297521 2.234929743801653 2.3356376694214878 45.863283870267786 0.8140906607528016 32.99998943844663 48.60011409208167 10.094791644327438 7.651563012286325 6.971378206070996 3.177230184347278 2.7661458768991785
user_001 Jogging 1.446047148981e12 12.79958 -0.650847 -9.69564 5.633772727272737e-2 1.442836727272727 -4.118291 163.82924817640003 0.42360181740899994 94.00543500959998 16.07041645395069 9.496347796961764 12.743242272727274 2.093683727272727 5.577348999999999 6.552456983471075 1.3722480165289257 3.4896825041322317 162.3902236214234 4.383511549846618 31.10682186780099 75.01246971118104 4.620914972535286 18.221982671141372 8.660973947032806 2.1496313573576487 4.268721432834587
user_001 Jogging 1.446047149102e12 3.90927 -19.58108 6.24561 6.884320090909092 -13.331385454545455 5.482689090909091 15.282391932899998 383.4186939664 39.0076442721 20.921489673811468 20.6720219868055 2.975050090909092 6.249694545454545 0.7629209090909095 3.4754289752066114 6.580958413223141 10.052906661157023 8.850923043418195 39.0586819114843 0.5820483135280998 18.677426649414937 52.092639445531944 133.3166367591787 4.321738845582289 7.217523082438459 11.546282378288636
user_001 Jogging 1.446047149231e12 9.35075 -7.51018 2.49022 8.326558181818182 -15.567899090909092 4.092707272727273 87.4365255625 56.4028036324 6.2011956484 12.249103021988997 18.352229744497517 1.0241918181818175 8.057719090909092 1.6024872727272728 1.0755028099173556 3.044405785123968 1.612303834710744 1.048968880430577 64.92683694800085 2.5679654592528927 2.035575883434261 18.39229401416228 3.28217159657215 1.4267360945298402 4.288623790234145 1.8116764602356983
user_001 Jogging 1.446047149264e12 11.11349 -2.6435 -2.0699 8.939681818181818 -10.05674090909091 2.490221 123.50965998010001 6.98809225 4.28448601 11.609575282502801 14.592364505757205 2.173808181818183 7.413240909090911 4.5601210000000005 1.1815951239669422 5.758498429752065 2.2574150991735538 4.725442011339674 54.95614077621904 20.794703534641005 2.1236015528734042 40.66845828931668 6.497162255694437 1.4572582313623774 6.377182629446697 2.5489531685957743
user_001 Jogging 1.44604714928e12 13.22111 -0.842448 -3.10454 9.89768909090909 -6.970213454545455 1.1037228181818184 174.7977496321 0.7097186327039999 9.638168611600001 13.60682317355539 13.2681391170847 3.3234209090909097 6.127765454545455 4.208262818181819 1.6344719834710744 6.779212396694215 2.755262090909091 11.045126538982649 37.549509465920664 17.709475946891583 3.6817334965635626 48.05599824849062 9.364926510827347 1.918784379903996 6.932243377759512 3.060216742459159
user_001 Jogging 1.446047149394e12 2.68302 -4.29128 2.49022 5.776515454545454 -0.11436245454545459 -1.007377090909091 7.1985963204 18.415084038400003 6.2011956484 5.640467711741643 6.993932828298204 3.0934954545454536 4.176917545454546 3.4975970909090908 4.619971983471075 2.365723818181818 2.9259617520661156 9.569714127293382 17.44664018152603 12.233185410335734 27.913373627294142 7.4033716166812065 13.02444588125051 5.283310858476353 2.7209137466449036 3.608939717043014
user_001 Jogging 1.446047149402e12 5.86361 -6.36057 5.55585 5.1494563636363635 -0.9643760909090912 -2.8467090909090942e-2 34.3819222321 40.4568507249 30.867469222500006 10.281354102427365 6.646319206470613 0.7141536363636369 5.396193909090909 5.584317090909091 4.641190991735538 2.4572493553719004 3.33323420661157 0.5100154163314058 29.11890870450982 31.184597371819375 27.93872818168933 8.299004545766735 15.748543563853593 5.285709808690724 2.880799289392917 3.9684434686478265
user_001 Jogging 1.446047149434e12 6.89825 -19.58108 9.04299 4.630389999999999 -7.005050545454545 2.9082616363636364 47.5858530625 383.4186939664 81.7756681401 22.644650917357946 10.195556118901754 2.2678600000000007 12.576029454545456 6.134728363636363 4.597170826446281 5.882325909090909 3.9169054380165282 5.143188979600003 158.15651684159488 37.634892095604485 26.575008670971535 50.825509825809554 21.491222617181755 5.155095408522672 7.129201205311122 4.635862661596195
user_001 Jogging 1.446047149563e12 3.98591 -15.74905 2.95007 11.92169909090909 -19.128203636363637 0.5080178181818181 15.8874785281 248.0325759025 8.702913004900001 16.511298175355567 23.144901652304863 7.93578909090909 3.379153636363636 2.442052181818182 5.774967107438017 0.8791501652892587 3.5599889008264465 62.97674849539172 11.418679298149584 5.963618858722944 41.11842897361307 2.1366249748332855 16.233832526013103 6.412365318165604 1.4617198687960993 4.029123046769992
user_001 Jogging 1.44604714962e12 -2.33694 -4.21464 -0.843646 2.188339454545454 -12.40473181818182 3.2217923636363635 5.461288563599999 17.7631903296 0.711738573316 4.892465377140241 13.428669191244422 4.525279454545454 8.19009181818182 4.065438363636363 6.705104636363637 4.739049917355373 2.9405300743801646 20.478154141731203 67.07760399024879 16.52778908852631 47.59374277461837 31.377978538409174 10.302701637973604 6.8988218396055405 5.601604996642406 3.209782179209923
user_001 Jogging 1.446047149669e12 -10.34589 -0.152682 0.152682 -5.040265090909091 -4.266891727272728 0.9608932727272728 107.03743989210001 2.3311793124000002e-2 2.3311793124000002e-2 10.34814299661287 8.821005416974698 5.30562490909091 4.114209727272727 0.8082112727272728 6.073611198347108 6.515719066115702 2.7058581157024792 28.149655675965928 16.926721679985526 0.653205461363438 38.210883633728024 44.103016009657594 9.257819553824516 6.181495258732148 6.641010164851248 3.042666520311504
user_001 Jogging 1.446047149782e12 8.00954 2.52974 -14.9072 -2.4971918181818182 1.1780775454545456 -3.1916349999999998 64.1527310116 6.3995844675999995 222.22461184 17.110725505343133 7.3390330778954285 10.506731818181818 1.3516624545454543 11.715565 3.812711074380165 0.9545242231404959 3.9469921652892554 110.3914134991942 1.8269913910278424 137.254463269225 20.90936161935897 1.1652671375526948 36.498496284713816 4.572675542760384 1.079475399234598 6.041398537152951
user_001 Jogging 1.446047149863e12 15.32872 -11.18893 -5.05888 8.033928999999999 -5.155224363636363 -3.5748378181818183 234.96965683840003 125.19215454489998 25.592266854400002 19.640623163171274 15.724526838982381 7.294791000000002 6.033705636363636 1.484042181818182 7.81702794214876 4.484109628099174 8.200230900826448 53.213975733681025 36.40560370628631 2.20238119741567 78.26415031479696 30.749846915804653 98.87448495723784 8.846702793402578 5.54525445005048 9.943565002414267
user_001 Jogging 1.446047149871e12 11.15181 -15.21256 16.7837 8.31958990909091 -6.768160727272726 -0.6938469090909084 124.36286627609998 231.4219817536 281.69258569 25.248315463010595 16.46430774422488 2.8322200909090895 8.444399272727274 17.477546909090908 7.11934505785124 5.128903884297521 8.724047438016528 8.021470643349092 71.30787907723692 305.46464595947316 68.9577918733565 37.06629125091457 114.16631974726042 8.304082843599074 6.088209199010376 10.684864049077106
user_001 Jogging 1.446047149944e12 9.38908 -19.58108 8.58315 6.636980909090909 -18.389666363636362 5.719578181818182 88.1548232464 383.4186939664 73.67046392249999 23.350459976953342 22.55196135090203 2.752099090909091 1.191413636363638 2.8635718181818177 2.407844991735537 5.750263537190083 6.912224115702478 7.574049406182646 1.4194664529132273 8.200043557885122 9.657153846656074 41.139247568377066 86.3043109583581 3.1075961524393856 6.413988429080385 9.290011354048934
user_001 Jogging 1.446047150016e12 6.51505 -13.14327 3.10335 7.936387272727271 -18.02736636363636 4.813826363636364 42.44587650249999 172.74554629289997 9.6307812225 14.994072296007511 20.44310503121508 1.4213372727272713 4.8840963636363615 1.7104763636363645 2.761913388429752 1.6195868595041334 1.1109719834710745 2.0201996428437976 23.85439728928593 2.9257293905586805 10.517149891811421 5.401965107519985 1.8010637061118713 3.2430155552836037 2.324212793080699 1.3420371478136779
user_001 Jogging 1.446047150073e12 17.89618 0.307161 -19.54396 8.793368181818183 -10.115964454545455 -2.2684658181818182 320.27325859240005 9.434787992100001e-2 381.96637248159993 26.501584461196295 16.630296665418793 9.102811818181818 10.423125454545456 17.275494181818182 2.970298512396694 5.750580082644627 4.936670809917355 82.86118299723059 108.64154424119342 298.4426992260339 17.678004749792333 38.80134902204815 65.50860297388387 4.204521940695795 6.229072886236615 8.09373850416999
user_001 Jogging 1.446047150219e12 7.51138 -8.12331 -0.383802 6.535954545454545 -0.10739454545454558 -3.163767454545454 56.4208295044 65.9881653561 0.147303975204 11.070514840589123 10.938402494551363 0.975425454545455 8.015915454545455 2.7799654545454544 3.8171466942148764 3.090644190082645 7.9747422314049565 0.9514548173752075 64.25490057442067 7.728207928466115 19.912643683929602 16.446861510478875 100.57568271687927 4.4623585337722025 4.0554730316547385 10.028742828334929
user_001 Jogging 1.446047150243e12 8.1245 -15.71073 7.20362 7.567119090909089 -4.44804 -3.1707347272727264 66.00750024999999 246.8270371329 51.8921411044 19.09781868400944 13.582559288601772 0.5573809090909103 11.26269 10.374354727272726 2.450916115702479 5.704342760330579 7.738803190082644 0.3106734778190096 126.84818603609999 107.62723600728596 11.5941647847275 46.82268835630012 97.03941247664534 3.405020526329834 6.842710600069253 9.850858463943402
user_001 Jogging 1.446047150268e12 12.41638 -19.4278 10.46085 8.852590909090909 -10.168218181818181 -5.2854727272726845e-2 154.1664923044 377.43941284000005 109.42938272250001 25.318674686225187 17.246433333074293 3.5637890909090917 9.25958181818182 10.513704727272728 2.286550661157025 8.188196363636363 8.710745471074379 12.70059268448265 85.73985544760333 110.53798709227691 10.773763729945234 76.44156760443937 104.44351299752908 3.282341196454938 8.7430868464427 10.2197609070628
user_001 Jogging 1.446047150284e12 10.80693 -19.58108 9.11964 8.702792727272728 -14.045537272727275 4.956656181818182 116.7897360249 383.4186939664 83.1678337296 24.15318330408851 17.820332107144218 2.1041372727272716 5.535542727272725 4.162983818181819 1.7776185950413228 8.856742892561984 6.789029223140495 4.427393662480161 30.64223328546196 17.330434270443675 4.639401814140121 82.55556567736312 59.70904086977294 2.1539270679714577 9.086009337292314 7.727162536777193
user_001 Jogging 1.446047150324e12 12.14814 -19.58108 4.29128 11.284189090909091 -18.926151818181815 5.541912636363636 147.57730545959998 383.4186939664 18.415084038400003 23.439519693551745 23.198834022657703 0.8639509090909083 0.6549281818181854 1.250632636363636 2.00912479338843 6.009955454545454 6.8473013553719 0.746411173319007 0.42893092333967403 1.5640819911378585 5.249374220344404 52.14090314037559 61.60130984272627 2.2911512870922346 7.220865816533055 7.848650192404186
user_001 Jogging 1.446047150405e12 1.07357 -10.42253 1.07237 6.981863636363636 -17.13903090909091 4.709316363636364 1.1525525448999998 108.6291316009 1.1499774169 10.532410054811766 19.27835656772833 5.908293636363636 6.716500909090909 3.6369463636363637 3.372187024793389 1.9901223966942168 1.179696619834711 34.90793369349504 45.11138446181901 13.227378851967769 14.967308917364766 8.682548946544332 2.3495476234109898 3.868760643586621 2.9466165251936554 1.5328234155997846
user_001 Jogging 1.446047150648e12 4.98224 -9.69444 13.948 6.37222090909091 -2.2289466363636365 -8.420690909090825e-2 24.8227154176 93.9821669136 194.546704 17.701739641379884 12.222252634351964 1.3899809090909097 7.465493363636364 14.032206909090908 6.154051157024793 3.024770818181818 7.538651479338842 1.9320469276371917 55.73359116249859 196.90283073953862 50.009996299928396 14.55400636162292 78.89689127763887 7.0717746216864406 3.8149713447970903 8.88239220467318
user_001 Jogging 1.446047150697e12 1.53341 -17.51178 5.55585 7.535765454545455 -9.994035454545456 3.1486354545454547 2.3513462280999997 306.6624387684001 30.867469222500006 18.435868686313647 16.111863223352596 6.002355454545455 7.517744545454546 2.4072145454545457 3.9055057851239665 6.042574842975207 8.693645363636366 36.02827100271158 56.51648305071158 5.7946818678479355 19.9161504314891 41.937659552253066 111.7926043798458 4.462751441822533 6.475929242375419 10.57320218192416
user_001 Jogging 1.446047150793e12 10.46204 -19.54276 6.24561 7.661177272727273 -19.535792727272725 5.656872090909091 109.4542809616 381.91946841760006 39.0076442721 23.030010717568068 22.099586635479316 2.800862727272727 6.967272727276708e-3 0.5887379090909093 2.9281772727272735 2.3704752066115735 2.3156854628099173 7.844832017025618 4.8542889256253815e-5 0.34661232560073574 12.87407932845424 9.62765954508025 7.460318108028584 3.588046728856 3.102847006392718 2.731358289940846
user_001 Jogging 1.446047150834e12 8.50771 -11.4955 2.8351 9.511003636363638 -17.368954545454542 3.9045884545454546 72.3811294441 132.14652025 8.03779201 14.579624196257598 20.393900266321058 1.0032936363636384 5.873454545454543 1.0694884545454544 2.6957220082644624 2.1975576033057864 1.385232033057851 1.0065981207677728 34.497468297520626 1.1438055544060244 12.06560516315159 8.839956388241845 2.4539926417881213 3.473557997666311 2.9732064153438533 1.5665224676933687
user_001 Jogging 1.446047151037e12 5.40376 -4.55952 -0.728685 4.024230909090909 -0.13526436363636377 -2.6272832727272726 29.2006221376 20.7892226304 0.530981829225 7.107800404993446 7.222132790105045 1.3795290909090907 4.424255636363636 1.8985982727272726 2.206425950413223 2.662786214876033 5.014576909090909 1.9031005126644622 19.5740379358954 3.6046754012029827 7.852155238665514 8.991493953473054 37.35349103853367 2.8021697376614276 2.9985819904536632 6.111750243468205
user_001 Jogging 1.446047151109e12 5.74865 -19.58108 6.16897 5.313188181818181 -13.79123 2.1592725454545456 33.04697682249999 383.4186939664 38.056190860899996 21.319518325933164 15.60131921150684 0.4354618181818184 5.7898499999999995 4.009697454545455 1.1201566115702482 7.893667628099174 4.2361372479338835 0.18962699509421507 33.522363022499995 16.077673676988297 1.8859984245438768 68.41907075554805 20.595874900877785 1.3733165784129588 8.271582119253127 4.538267830447844
user_001 Jogging 1.446047151206e12 1.68669 -14.5228 4.7128 7.905035454545454 -18.184130909090907 0.5498201818181818 2.8449231561 210.91171984000002 22.21048384 15.361221528123993 20.60780788439442 6.218345454545455 3.661330909090907 4.162979818181817 4.84134479338843 1.2287837190082649 3.097295462809917 38.66782019206612 13.405344025864448 17.330400966589117 28.15586054618888 3.1095243914700963 17.112671343026122 5.306209621395378 1.763384357271578 4.136746468304061
user_001 Jogging 1.446047151312e12 -3.33327 0.613724 -1.11189 -0.23629118181818212 -3.733888636363637 0.23977381818181834 11.1106888929 0.37665714817600005 1.2362993721000002 3.567021924964297 5.887372545391934 3.096978818181818 4.347612636363637 1.3516638181818184 2.5582775619834717 6.220242198347108 2.9696667768595044 9.59127780026685 18.901735635868775 1.8269950773818517 10.102695203948885 39.87971431446006 10.319315675667944 3.178473722393955 6.315038742118694 3.212369168646086
user_001 Jogging 1.446047151352e12 -0.267643 4.21583 -1.91661 -1.9084504545454544 0.4639268181818181 -1.063117090909091 7.163277544900001e-2 17.773222588900005 3.6733938920999996 4.638776698273911 3.685062453253754 1.6408074545454543 3.7519031818181823 0.8534929090909089 2.8578729834710743 4.62060579338843 2.3017529421487604 2.692249102891933 14.0767774857374 0.7284501458684625 10.69858823466386 22.2415387209836 7.617826076039722 3.2708696450124486 4.7160935869619465 2.760040955500429
user_001 Jogging 1.446047151417e12 6.9749 -0.344284 8.19995 2.5680608181818183 3.209053363636363 -3.9232039090909097 48.64923001 0.11853147265599999 67.23918000249999 10.770651859806629 9.713949174801307 4.406839181818182 3.553337363636363 12.12315390909091 3.6635484710743795 3.071323785123967 6.242726438016529 19.42023157440794 12.62620641981422 146.9708607035062 19.565297848868102 10.906363885450785 60.51857971860243 4.423267779466681 3.302478445872249 7.779368850916019
user_001 Jogging 1.446047151578e12 9.54236 -19.58108 2.60518 4.891664545454546 -19.56714545454545 4.1031581818181815 91.0566343696 383.4186939664 6.7869628323999995 21.93769110841886 21.159088532938316 4.650695454545454 1.3934545454549863e-2 1.4979781818181817 4.304542066115702 4.257987305785124 1.9438857024793388 21.628968210929752 1.9417155702491625e-4 2.2439386332033053 26.518021072216154 29.578972161291038 6.378130290521789 5.1495651342823265 5.43865536334957 2.5254960484074784
user_001 Jogging 1.446047151635e12 3.29615 -12.56846 4.63616 7.093340909090909 -17.65113 3.9045881818181813 10.864604822499999 157.9661867716 21.493979545600002 13.795824409570455 19.577262417347413 3.797190909090909 5.0826699999999985 0.7315718181818189 2.8806734710743807 1.836841239669422 1.3944159504132232 14.418658800082643 25.833534328899983 0.5351973251578523 10.559005899553947 6.313381829459578 2.739620745666492 3.2494624016218356 2.5126443897733672 1.6551799737993727
user_001 Jogging 1.446047151724e12 6.82161 2.91294 -5.4804 7.260554545454545 -3.1416661818181826 -2.338138363636364 46.53436299209999 8.485219443599998 30.034784160000005 9.222492428606271 9.907660701299607 0.43894454545454487 6.054606181818182 3.1422616363636364 1.4650392561983472 7.173182066115704 4.107240454545455 0.19267231398429702 36.65825601691095 9.873808191362677 2.9706421240818184 51.96965262163333 20.13785207873389 1.7235550829845323 7.2089980317401485 4.487521819304491
user_001 Jogging 1.446047151733e12 7.62634 3.94759 -5.02056 7.518345454545454 -1.7969716363636365 -3.101061090909091 58.1610617956 15.583466808099999 25.206022713599996 9.94738917089806 9.691493439543757 0.10799454545454612 5.7445616363636365 1.9194989090909087 1.2918062809917357 7.148796347107439 4.224101760330578 1.1662821847934029e-2 32.999988393980864 3.6844760620011887 2.6031193905631858 51.68294079364623 20.43626016398501 1.6134185416571813 7.189084837004375 4.520648201749945
user_001 Jogging 1.446047151741e12 7.24314 4.40743 -4.21583 7.685561818181816 -0.5985916363636367 -3.7246365454545454 52.4630770596 19.425439204899998 17.773222588900005 9.468988269788913 9.585143130985788 0.44242181818181603 5.006021636363636 0.49119345454545504 1.2357502479338842 6.958460958677687 4.146827280991736 0.1957370652033039 25.060252623740855 0.24127100978829802 2.5189534991681444 49.37879148738046 20.294661930347736 1.5871211356314754 7.02700444623315 4.504959703520969
user_001 Jogging 1.446047151781e12 4.48408 2.52974 -1.91661 6.466280000000001 2.944294727272727 -4.0068127272727265 20.106973446399998 6.3995844675999995 3.6733938920999996 5.493628291584715 8.398280777683723 1.9822000000000015 0.41455472727272724 2.0902027272727266 1.1502414876033058 4.31594256198347 2.787565033057851 3.929116840000006 0.17185562190416526 4.368947441098344 1.8744906532619081 24.103478716583982 11.197507370263382 1.3691203939982444 4.909529378319676 3.346267677616867
user_001 Jogging 1.44604715191e12 9.77228 -19.50444 1.53221 4.724448181818182 -13.442863636363633 1.4625413636363638 95.4974563984 380.42317971359995 2.3476674841 21.86934620870272 15.13713907118882 5.047831818181819 6.061576363636366 6.96686363636363e-2 1.8713614049586773 7.98075973553719 4.206682272727272 25.480606064648764 36.74270801219507 4.8537188927685855e-3 5.178756076771825 67.91527688974624 23.678325446133485 2.2756880446958947 8.241072557000468 4.866037961846731
user_001 Jogging 1.446047151951e12 10.92189 -19.58108 1.8771 9.577193636363639 -18.46630818181818 0.8528991818181818 119.2876811721 383.4186939664 3.52350441 22.49955287441286 21.701183277391326 1.344696363636361 1.1147718181818185 1.0242008181818183 3.7595082644628093 5.658104900826447 5.013626694214876 1.8082083103768523 1.2427162066123973 1.048987315964306 24.23546088704974 43.77931753685487 35.968189974079955 4.922952456306047 6.616594103982416 5.997348578670407
user_001 Jogging 1.446047151976e12 4.25415 -19.58108 4.67448 10.047488181818183 -19.225746363636357 1.0549519090909092 18.0977922225 383.4186939664 21.850763270399998 20.57589000406301 22.60094362279498 5.793338181818183 0.35533363636364257 3.619528090909091 4.706749008264463 3.0827260330578525 4.312143818181818 33.56276728891241 0.12626199313140937 13.100983600880006 29.278619037157853 16.794070458794213 28.49283913515609 5.410972097244437 4.098056912586038 5.337868407440941
user_001 Jogging 1.446047152016e12 4.48408 -14.98264 6.05401 7.438222727272728 -18.466307272727274 3.2914646363636364 20.106973446399998 224.4795013696 36.6510370801 16.77013750379227 20.591913786123246 2.9541427272727283 3.483667272727274 2.7625453636363635 4.226635619834712 1.3982168595041338 2.6770381157024796 8.726959253098354 12.135937667071085 7.631656886148768 20.821342925891145 3.0201815245361403 8.235197835964952 4.563040973505623 1.7378669467298526 2.8697034404211443
user_001 Jogging 1.446047152064e12 1.87829 -2.8351 -1.53341 3.9789436363636366 -11.882180000000004 2.9535480000000005 3.5279733241 8.03779201 2.3513462280999997 3.7305645098563835 13.13876244651408 2.100653636363637 9.047080000000003 4.4869580000000004 2.783764876033059 5.077600413223141 2.743226958677686 4.41274569996777 81.84965652640005 20.132792093764003 10.053849827812401 36.27602943311487 8.753824143514345 3.1707806338207 6.022958528257925 2.958686219171331
user_001 Jogging 1.446047152089e12 -1.95374 -0.229323 -1.72501 2.4844516363636364 -7.1304620909090906 1.6715598181818179 3.8170999876000002 5.2589038329e-2 2.9756595001 2.616361696331186 8.520474343812703 4.438191636363636 6.901139090909091 3.396569818181818 2.494937132231405 6.901456363636364 3.1270625537190084 19.69754500108813 47.62572075207355 11.536686529783667 7.469635887459421 51.97030174191706 11.108772798224885 2.7330634620256116 7.209043053132438 3.3329825679449456
user_001 Jogging 1.446047152121e12 -7.1653 2.41478 -1.26517 -0.9608938181818183 -1.619304454545455 -0.8958999090909091 51.34152409 5.8311624484 1.6006551288999997 7.66637734965479 5.000751755683819 6.204406181818182 4.034084454545455 0.3692700909090908 3.5713902892561977 7.143729504132231 2.8534371157024796 38.49465606898367 16.273837386405297 0.13636040004000818 16.102131490102952 53.84664377135873 10.161223564866225 4.012746128289572 7.338027239753115 3.1876674175431514
user_001 Jogging 1.446047153934e12 7.47306 -7.51018 2.52854 4.94740290909091 -6.4894690909090915 -0.23400418181818186 55.8466257636 56.4028036324 6.3935145316 10.89233418178124 11.335213146620982 2.52565709090909 1.0207109090909086 2.762544181818182 3.6483468760330577 7.761921628099173 2.983284371900827 6.378943740859366 1.041850759937189 7.631650356497488 17.440279192640055 74.55776113851049 11.886500614431673 4.1761560306866 8.634683615426248 3.4476804687255567
user_001 Jogging 1.446047154257e12 4.17751 0.307161 0.650847 5.1006838181818175 -7.677398090909091 0.23280609090909074 17.4515898001 9.434787992100001e-2 0.42360181740899994 4.239049362466778 12.33218067780529 0.9231738181818177 7.984559090909091 0.4180409090909092 3.599259553719008 8.311389859504134 3.1143959008264472 0.8522498985763958 63.753183876219005 0.1747582016735538 17.226113662722206 86.6462533486209 15.967773060603179 4.150435358215112 9.308396926894604 3.995969602061955
user_001 Jogging 1.44604715471e12 9.00587 -2.22198 -1.49509 5.100684 -7.464894272727275 -0.5545014545454546 81.1056944569 4.937195120399999 2.2352941081 9.395647060495621 11.52705378980653 3.9051859999999996 5.242914272727274 0.9405885454545454 3.9270390578512395 7.693831363636364 1.828923950413223 15.250477694595997 27.488150071167365 0.8847068118402974 21.882637782047397 70.36756291734724 7.930507014658335 4.67788817545347 8.388537591102947 2.81611558971899
user_001 Jogging 1.446047154905e12 6.74497 -15.40417 3.48655 4.529362181818183 -9.478453363636364 0.7449061818181818 45.4946203009 237.28845338890002 12.1560309025 17.173791211968894 12.247786756547718 2.2156078181818177 5.925716636363637 2.741643818181818 3.307896446280992 8.032380694214877 1.6208546280991738 4.908918003988394 35.11411765447677 7.5166108257745785 17.328900067769936 72.46294735240768 4.432801456994455 4.162799546911902 8.512517098508976 2.1054219189973433
user_001 Jogging 1.44604715497e12 5.86361 -4.7128 0.650847 4.682644000000001 -9.934813454545456 0.7449061818181818 34.3819222321 22.21048384 0.42360181740899994 7.550894509229288 12.548863588071583 1.1809659999999997 5.222013454545456 9.405918181818185e-2 3.3313320991735536 7.781240181818182 1.591401743801653 1.3946806931559994 27.269424519453768 8.847129684305791e-3 17.378211958186263 69.14624195633812 4.41771863226816 4.16871826322987 8.315421934955442 2.1018369661484595
user_001 Jogging 1.446047155164e12 5.59536 -16.13225 3.7722e-2 4.355179454545455 -6.994599818181817 8.649363636363634e-2 31.308053529600002 260.24949006249994 1.422949284e-3 17.075097848662068 10.670622017712152 1.2401805454545451 9.13765018181818 4.877163636363634e-2 3.3595184628099175 7.907918900826448 1.9141160082644626 1.5380477853239332 83.49665084528183 2.3786725135867747e-3 16.90470911643385 71.7752335717931 6.28171303261849 4.111533669621817 8.472026532760216 2.506334581140054
user_001 Jumping 1.446047227671e12 0.575403 -0.727487 2.95007 2.4530965 -6.7246185 -0.11555499999999985 0.331088612409 0.529237335169 8.702913004900001 3.092448698439151 8.451269086203546 1.8776935 5.9971315 3.065625 0.93884675 2.99856575 1.5328125 3.52573287994225 35.96558622829225 9.398056640624999 1.762866439971125 17.982793114146126 4.699028320312499 1.3277298068399026 4.240612351317452 2.1677242260750096
user_001 Jumping 1.446047228771e12 5.63368 -19.58108 5.59417 2.6865030909090906 -9.102216272727274 1.904966727272727 31.7383503424 383.4186939664 31.2947379889 21.129405630488048 10.699369611977787 2.9471769090909095 10.478863727272726 3.6892032727272728 2.3082646342516067 7.828420587603304 1.485286929476584 8.685851733478646 109.80658501475205 13.61022078750162 7.602895554261843 72.41129287122205 4.47538958087852 2.757334864368462 8.509482526641795 2.1155116593577357
user_001 Jumping 1.446047229678e12 1.64837 -0.727487 -0.307161 1.7702999999999998 -6.9388619090909085 0.6334268181818182 2.7171236568999997 0.529237335169 9.434787992100001e-2 1.8277606167083258 8.146417896575903 0.12192999999999987 6.2113749090909085 0.9405878181818182 1.3057419917355373 6.445413867768594 0.7844572066115703 1.4866924899999969e-2 38.581178261284094 0.8847054437120332 2.9860285836722325 51.402171643057116 0.9434764262345948 1.7280129003199693 7.169530782628464 0.9713271468638127
user_001 Jumping 1.446047229743e12 2.56806 -1.03405 0.267643 1.8504245454545454 -6.945829272727272 0.5149825454545455 6.5949321636 1.0692594024999997 7.163277544900001e-2 2.7813349926876842 8.172391978699084 0.7176354545454546 5.911779272727272 0.24733954545454545 1.3551465785123966 6.545490115702479 0.7524711818181818 0.5150006456206613 34.949134169447795 6.1176850745661156e-2 3.0300886047082014 52.47526121010706 0.9163994449650903 1.7407149694042967 7.243981033251472 0.9572875456022032
user_001 Jumping 1.44604723039e12 2.68302 0.268841 0.535886 2.156987 -6.151554090909091 0.6194927272727272 7.1985963204 7.2275483281e-2 0.287173804996 2.749189991375096 7.848112788192466 0.526033 6.420395090909091 8.360672727272722e-2 2.190274570247934 6.47613232231405 0.7508874214876033 0.27671071708899997 41.221473123369556 6.990084845256189e-3 7.960874463777737 50.38179048260929 1.1474568828624658 2.8215021644113154 7.0980131362663235 1.071194138736049
user_001 Jumping 1.446047231296e12 11.61165 -19.58108 4.25296 3.6932826363636355 -7.416123636363636 0.5672378181818182 134.8304157225 383.4186939664 18.0876687616 23.158945970196918 9.36085068307741 7.918367363636364 12.164956363636364 3.6857221818181816 3.0409216446280993 7.26154073553719 1.760200305785124 62.70054170550149 147.98616332917686 13.584548001546576 12.618763656560139 62.25575293517845 3.835529500171806 3.5522899173012523 7.890231488060312 1.9584507908476552
user_001 Jumping 1.446047231555e12 -0.919089 -0.382604 0.114362 2.867653454545455 -6.116717181818182 0.5776896363636365 0.8447245899210001 0.146385820816 1.3078667044000002e-2 1.0020923499263927 8.397198505817867 3.786742454545455 5.7341131818181825 0.46332763636363644 3.6160431239669424 7.249506231404959 1.7985207438016528 14.339418417056937 32.88005398190104 0.2146724986183141 15.941718766454512 64.06415040944202 4.433685351168226 3.99270819951252 8.004008396387526 2.1056318175712074
user_001 Jumping 1.446047232332e12 1.45677 -0.957409 0.420925 2.8606881818181815 -6.423278727272727 -0.7321674545454546 2.1221788328999995 0.9166319932809999 0.177177855625 1.7933177860619125 8.07830938399036 1.4039181818181816 5.465869727272727 1.1530924545454546 1.8216388347107435 6.94674379338843 1.2500011074380166 1.970986261239669 29.875731875516436 1.3296222087296614 5.385024996212779 55.70059721558134 2.283652852964922 2.3205656629823643 7.463283273170149 1.5111759834529273
user_001 Jumping 1.446047232397e12 1.18853 -2.95007 0.650847 2.84327 -6.649717363636362 -0.7008144545454547 1.4126035609000003 8.702913004900001 0.42360181740899994 3.246400835264956 8.238312707705102 1.6547399999999999 3.6996473636363616 1.3516614545454546 1.8213221900826446 6.764009280991735 1.3415265041322315 2.7381644675999994 13.687390615261481 1.826988687703934 5.383975964246953 53.981179779284275 2.438929673971659 2.320339622608499 7.347188562932374 1.5617072945887327
user_001 Jumping 1.446047233692e12 1.91661 -2.95007 -0.345482 2.4530986363636362 -6.485985363636365 0.1108783636363636 3.6733938920999996 8.702913004900001 0.119357812324 3.534920750076867 7.642951055439692 0.5364886363636363 3.5359153636363647 0.4563603636363636 1.7491166859504133 6.342802719008264 0.7968080991735537 0.287820056947314 12.502697458799686 0.20826478149831404 5.789309919787663 48.261592607761735 0.9506238958732367 2.406098485055768 6.947056398775077 0.9749994337809826
user_001 Jumping 1.446047233755e12 4.75232 -14.63776 -3.67935 2.6690859090909087 -7.51714990909091 -9.117436363636361e-2 22.5845453824 214.2640178176 13.5376164225 15.823595660357984 8.689111065763383 2.0832340909090914 7.12061009090909 3.588175636363636 1.9223500247933885 6.688635768595042 1.0153291322314049 4.3398642775258285 50.70308806675636 12.875004397393585 6.1809734275535115 51.871071733025275 1.99354172880025 2.486156356216059 7.202157436006607 1.411928372404298
user_001 Jumping 1.446047234273e12 1.11189 -0.152682 1.83878 2.8850731818181816 -5.9042141818181815 -1.0387308181818182 1.2362993721000002 2.3311793124000002e-2 3.3811118884000004 2.1542337509249085 7.883338389741368 1.7731831818181816 5.751532181818181 2.8775108181818183 1.935018611570248 6.829566181818181 1.9438862644628097 3.1441785962828503 33.08012243849021 8.280068508753397 7.562639685647951 53.59971111397245 5.921171536456791 2.75002539727326 7.321182357650467 2.433345749468577
user_001 Jumping 1.446047235892e12 2.79798 -9.88604 -0.843646 2.5436736363636365 -6.792547727272727 -0.22703800000000005 7.8286920804 97.7337868816 0.711738573316 10.308938720126141 8.932443619128527 0.2543063636363634 3.0934922727272722 0.6166079999999999 2.782497404958678 6.824814438016529 1.274070082644628 6.467172658595029e-2 9.569694441423344 0.3802054256639999 12.44456348689605 56.63568852073141 2.3675355543652423 3.5276852873939943 7.525668642767326 1.5386798089158258
user_001 Jumping 1.446047236475e12 7.58802 -18.54643 3.10335 3.8918525454545456 -8.22433409090909 0.22583972727272725 57.578047520400006 343.9700657449 9.6307812225 20.277546559872572 9.852919901323235 3.6961674545454546 10.32209590909091 2.8775102727272728 3.0387060082644624 7.119976330578512 1.2436688099173556 13.661653852041026 106.5456639564713 8.280065369650984 13.376589391758433 61.73144706318171 2.1075806428934363 3.6574020002945304 7.856936238966288 1.451750888717977
user_001 Jumping 1.44604723654e12 0.767005 -6.28393 0.689167 3.000034818181818 -7.029436818181818 0.4313758181818182 0.5882966700250001 39.4877762449 0.47495115388899994 6.36796859829051 8.41581035264782 2.233029818181818 0.7455068181818181 0.2577911818181818 2.5535269834710745 6.1192146776859495 1.1641781074380164 4.986422168889123 0.5557804159555784 6.645629342321485e-2 8.620365385624313 49.222535047066316 1.9970901490347777 2.9360458759400054 7.015877354049621 1.4131844002234024
user_001 Jumping 1.446047236669e12 0.11556 -0.114362 -1.11189 2.7248254545454547 -5.9285986363636365 0.25719245454545453 1.3354113599999998e-2 1.3078667044000002e-2 1.2362993721000002 1.1237135545787458 7.6763875816918326 2.6092654545454548 5.814236636363637 1.3690824545454545 2.8306369256198347 6.579058876033057 1.2154832396694213 6.808266212284298 33.805347663633135 1.8743867673442065 9.500612024374687 54.4232190659533 2.0968215239484818 3.082306283349318 7.37720943622677 1.4480405809052734
user_001 Jumping 1.446047238481e12 -0.152682 -1.41725 -1.22685 2.965196909090909 -5.3712112727272725 -9.465809090909091e-2 2.3311793124000002e-2 2.0085975625 1.5051609225 1.8807100462655055 7.1786868769543135 3.117878909090909 3.9539612727272724 1.1321919090909092 2.806566479338843 6.916658347107438 0.8180279834710745 9.721168891753916 15.633809746227072 1.2818585190109175 11.351055486512807 57.72618438699079 0.722933934470577 3.3691327499095087 7.597774962907943 0.8502552172557232
user_001 Jumping 1.4460472401e12 0.996927 3.8919e-2 -0.575403 2.8502368181818176 -5.782284454545455 -0.1294945454545454 0.993863443329 1.514688561e-3 0.331088612409 1.1517233801130375 7.488380834527844 1.8533098181818177 5.821203454545455 0.4459084545454546 2.339439314049587 6.414693702479339 1.1030548595041323 3.434757282169122 33.88640965921194 0.19883434983511572 7.295192824921782 51.8848540825245 1.7815078835544063 2.700961463057513 7.20311419335585 1.3347313900386124
user_001 Jumping 1.446047240295e12 7.39642 -19.58108 1.11069 3.553936818181818 -7.583338636363636 4.817236363636368e-2 54.7070288164 383.4186939664 1.2336322760999998 20.960900626139612 9.373704248824843 3.842483181818182 11.997741363636365 1.0625176363636362 2.5554266694214878 7.10002667768595 1.1068550661157026 14.76467700255558 143.945797828711 1.1289437275837682 8.508716858026242 63.728283208053945 1.7536987839118117 2.91697049317031 7.982999637232482 1.3242729265192321
user_001 Jumping 1.446047241459e12 -0.765807 -1.41725 7.6042e-2 2.278915636363636 -6.360573545454546 0.5358855454545455 0.586460361249 2.0085975625 5.782385764e-3 1.6127120975279499 8.104703046272826 3.044722636363636 4.943323545454546 0.4598435454545455 2.9804321652892556 7.0712062975206615 1.907149148760331 9.27033593238513 24.4364476750453 0.21145608629620663 10.990495416205771 58.02346179023377 6.027803224777757 3.315191610782968 7.617313292115125 2.4551584928019934
user_001 Jumping 1.446047242042e12 -0.995729 0.460442 0.305964 2.6307664545454545 -5.716095636363637 1.1420436363636361 0.991476241441 0.21200683536400003 9.361396929600001e-2 1.1389016841242268 7.747039606303429 3.6264954545454544 6.176537636363637 0.8360796363636361 3.649297107438016 6.35737238016529 2.1823569752066114 13.151469281838843 38.1496171734165 0.69902915834195 16.822933334173815 47.906882437427655 9.32110861503425 4.101576932616749 6.921479786680566 3.0530490685598637
user_001 Jumping 1.446047243531e12 11.57333 -19.58108 0.344284 4.5014933636363645 -7.2245218181818185 4.817318181818176e-2 133.9419672889 383.4186939664 0.11853147265599999 22.748168997261207 9.614007130330195 7.071836636363636 12.356558181818182 0.2961108181818182 3.602741462809917 7.240955603305786 1.341211165289256 50.01087341141494 152.68453010065784 8.768161664430581e-2 18.025288293019972 62.05824709530112 2.6538719664479 4.245619895023573 7.877705699967543 1.6290708905532318
user_001 Jumping 1.446047243855e12 -0.535886 -0.957409 1.18733 3.3867207272727273 -5.573264727272727 0.3268666363636364 0.287173804996 0.9166319932809999 1.4097525289 1.6166503416561664 7.784189991593638 3.9226067272727274 4.615855727272727 0.8604633636363637 3.7680581983471075 6.829566041322314 0.9785924380165288 15.386843536845257 21.306124094996438 0.740397200160405 20.30549192921104 54.09496022705587 1.5180806496353243 4.506161551610311 7.354927615351213 1.2321041553518617
user_001 Jumping 1.446047244373e12 -0.535886 -1.18733 1.64717 4.111323636363637 -5.952984272727273 -0.17478236363636365 0.287173804996 1.4097525289 2.7131690089 2.10002270054302 8.42056546855258 4.647209636363637 4.765654272727272 1.8219523636363637 3.491582256198347 6.728223553719008 0.8411461652892562 21.596557404311042 22.711460647163708 3.3195104153601327 18.261239277957863 53.18916722596664 1.0814781705921834 4.273317128175472 7.293090375551824 1.0399414265198705
user_001 Standing 1.446047262759e12 1.41845 -9.11964 0.305964 1.41845 -9.11964 0.305964 2.0120004025 83.1678337296 9.361396929600001e-2 9.234362354889265 9.234362354889265 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
user_001 Standing 1.446047263664e12 0.613724 -9.6178 0.229323 1.0387312727272728 -9.384396363636363 0.3930553636363637 0.37665714817600005 92.50207684000002 5.2589038329e-2 9.640089368180412 9.456826268521324 0.4250072727272728 0.23340363636363826 0.16373236363636368 0.23116370721500726 9.653719375573999e-2 0.16283225243342514 0.18063118187107444 5.447725746776948e-2 2.6808286901950425e-2 8.253073051903255e-2 1.3798900617681253e-2 3.6981783747246e-2 0.2872816223134236 0.11746872186961622 0.19230648389288907
user_001 Standing 1.446047263988e12 1.45677 -9.08132 -0.575403 0.9516397272727274 -9.391362727272728 0.23629054545454545 2.1221788328999995 82.47037294239999 0.331088612409 9.215402345405707 9.459287967285888 0.5051302727272725 0.3100427272727284 0.8116935454545454 0.33731404958677685 0.2481306611570256 0.28309523966942146 0.2551565924255287 9.612649273471145e-2 0.6588464117325702 0.16787532121653645 0.12819331652524443 0.13775742846689407 0.4097259098672385 0.358040942526472 0.37115687851216506
user_001 Standing 1.446047265736e12 1.03525 -9.46452 -0.613724 0.9934438181818183 -9.373945454545453 -0.27580827272727276 1.0717425625 89.5771388304 0.37665714817600005 9.540730503534622 9.43637041659947 4.180618181818174e-2 9.057454545454746e-2 0.3379157272727273 0.18526814049586776 0.12287735537190142 0.2039529008264463 1.7477568382148697e-3 8.203748284297884e-3 0.11418703873825621 5.9142881348738546e-2 1.964663117896333e-2 5.5500906570311793e-2 0.24319309478013257 0.1401664409870042 0.23558630386826776
user_001 Standing 1.446047265929e12 0.958607 -9.34956 -0.230521 0.9795095454545454 -9.384396363636363 -0.32806318181818184 0.918927380449 87.41427219360001 5.3139931441e-2 9.401400933131722 9.44541709001559 2.0902545454545396e-2 3.483636363636222e-2 9.754218181818183e-2 0.13142985950413222 9.595834710743874e-2 0.1992023388429752 4.369164064793364e-4 1.2135722314048601e-3 9.514477233851243e-3 2.979612839872803e-2 1.4155768455597456e-2 5.6693495851969186e-2 0.17261555086007757 0.11897801669046873 0.23810396017699745
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user_002 Jogging 1.446034901891e12 -2.68182 -7.6042e-2 0.995729 -2.866457272727273 0.28625900000000004 -0.9202861818181817 7.192158512400001 5.782385764e-3 0.991476241441 2.861715768486626 3.8984117439855948 0.1846372727272727 0.36230100000000004 1.9160151818181816 0.8411455785123967 2.412912652892562 2.5782283223140494 3.409092248016528e-2 0.13126201460100004 3.6711141769577598 1.2003020330379224 8.579598918568538 7.813035155574325 1.095582964926857 2.9290952389037366 2.795180701774811
user_002 Jogging 1.446034902086e12 -12.18526 -5.82409 -3.90927 -15.679373636363636 -11.188933636363636 -7.281458181818183 148.4805612676 33.9200243281 15.282391932899998 14.059977863730795 20.738969766811962 3.494113636363636 5.364843636363636 3.3721881818181836 1.291173578512396 2.5475080991735535 2.0585292561983475 12.208830103822311 28.7815472426314 11.371653133594227 3.1528208578917405 9.549293706104132 6.302081652987829 1.7756184437800089 3.0901931502907924 2.5103947205544848
user_002 Jogging 1.446034902093e12 -10.84405 -5.36425 -3.0279 -15.156823636363638 -10.258795454545453 -6.63698 117.59342040249999 28.7751780625 9.16817841 12.471438444501901 19.607507902411463 4.312773636363639 4.894545454545453 3.6090800000000005 1.361796363636363 2.6593016528925615 1.946102314049587 18.600016438513247 23.956575206611554 13.025458446400004 3.7071176739448544 10.506175181325467 5.351528005717207 1.925387668482598 3.241323060314332 2.313336984902374
user_002 Jogging 1.446034902134e12 -4.7128 -1.53221 -3.8919e-2 -11.13319181818182 -5.541913636363636 -3.292661363636364 22.21048384 2.3476674841 1.514688561e-3 4.955770980650841 12.951905235740183 6.42039181818182 4.009703636363636 3.253742363636364 3.776608512396695 4.219351074380165 2.819235206611571 41.22143109897605 16.077723251467763 10.586839368921954 18.97191993703419 18.784659065863558 9.502431067894996 4.3556767484553065 4.334127255384129 3.0826013475464187
user_002 Jogging 1.446034902207e12 1.57173 1.22685 -1.15021 -1.2779061818181818 1.5125097272727273 -0.7844235454545454 2.4703351929000004 1.5051609225 1.3229830441 2.3018425574960597 3.8283394853389723 2.849636181818182 0.28565972727272726 0.36578645454545455 5.201743809917356 3.6169951900826445 1.362746347107438 8.120426368727308 8.160147978552892e-2 0.13379973032893389 28.055339392748365 15.483652908929882 3.2315638527796566 5.296729122085475 3.9349273066893984 1.7976550983933643
user_002 Jogging 1.446034902231e12 -1.57053 -0.344284 -1.11189 -0.11784572727272725 1.8573923636363632 -1.1467244545454547 2.4665644809 0.11853147265599999 1.2362993721000002 1.9548389513348663 2.9538514725909635 1.4526842727272726 2.201676363636363 3.483445454545464e-2 3.776608099173554 2.949714570247934 0.648277909090909 2.110291596229165 4.847378810195039 1.2134392234793455e-3 17.801429361908134 11.44855536925793 0.6513529155226738 4.219174014177199 3.383571392664551 0.8070643812749227
user_002 Jogging 1.446034902256e12 -3.83143 -3.06503 0.765807 -0.5184667272727271 0.7217173636363636 -0.955123 14.6798558449 9.3944089009 0.586460361249 4.965956615502093 3.1629018655347987 3.312963272727273 3.7867473636363638 1.72093 3.1571484297520653 2.450917454545454 0.6970493388429753 10.975725646439804 14.339455596006951 2.9616000649000003 12.507239421669167 7.526855335243767 0.6687449028157296 3.5365575665707984 2.743511497195477 0.8177682451744686
user_002 Jogging 1.446034902345e12 -15.97897 -10.69077 6.39889 -5.165675545454545 -10.286663636363636 1.2361025454545453 255.3274822609 114.2925631929 40.945793232099994 20.26242430426083 12.469106604092127 10.813294454545456 0.4041063636363642 5.162787454545454 3.1954709173553724 5.691991082644628 2.7904146694214877 116.92733696070351 0.16330195313140541 26.65437430081193 25.07221924340757 44.56485109069431 11.683520211182929 5.007216716241426 6.675691057163618 3.4181164712722896
user_002 Jogging 1.446034902498e12 -6.82042 -10.001 -1.83997 -16.61648272727273 -13.056175454545455 -2.1430520000000004 46.51812897640001 100.020001 3.3854896009 12.244330099164266 21.356799196416535 9.796062727272728 3.0551754545454557 0.3030820000000003 5.281235619834711 2.6536024793388435 0.7819239338842976 95.96284495666201 9.334097058057031 9.185869872400018e-2 33.41177882625298 8.344735970507742 0.8624901692798557 5.780292278618182 2.888725665498152 0.9287034883534441
user_002 Jogging 1.446034902563e12 -6.13065 2.56806 -0.843646 -5.507074545454545 -5.120387272727272 -1.7145605454545458 37.5848694225 6.5949321636 0.711738573316 6.700114936284003 8.609060382124232 0.6235754545454553 7.688447272727272 0.8709145454545458 6.654433884297521 5.132704710743802 0.6333935123966944 0.38884634751157116 59.112221465507425 0.7584921454842982 56.966221893599545 28.942580369569132 0.4629910177542008 7.5475970940160515 5.379830886707233 0.6804344331044695
user_002 Jogging 1.446034902636e12 -1.91542 -3.21831 -0.805325 -4.4550090909090905 2.167436727272727 -3.0209355454545457 3.6688337763999996 10.357519256099998 0.6485483556249999 3.830783390916928 6.343693907563632 2.5395890909090904 5.385746727272727 2.215610545454546 0.8652156198347104 4.714664330578511 1.6072363801652896 6.44951275066446 29.006267810328886 4.90893008912939 1.2775306625186316 27.85260437570646 3.7260181570074264 1.1302790197639836 5.277556667218881 1.9302896562452554
user_002 Jogging 1.446034902724e12 -10.72909 -13.06663 -2.18486 -2.8072346363636367 -8.112857272727272 -0.1643308181818182 115.11337222809999 170.7368195569 4.7736132196000005 17.047692072670717 9.016976973428022 7.921855363636363 4.953772727272728 2.0205291818181816 3.2974469504132227 5.105151702479339 2.174439933884298 62.755792402374205 24.539864233471082 4.0825381745788505 15.810664296136576 26.721917705194425 5.090688727973939 3.9762626040210893 5.1693246856039545 2.256255466026385
user_002 Jogging 1.446034902838e12 -14.75272 -6.20729 -5.63368 -16.456233636363635 -10.419043636363636 -6.685749999999999 217.6427473984 38.530449144100004 31.7383503424 16.967956473450183 20.801511960308556 1.7035136363636347 4.211753636363635 1.0520699999999987 3.477331760330579 2.66595388429752 2.398978809917355 2.9019587092768537 17.738868693422305 1.1068512848999974 16.279098479944164 8.922266403834108 8.364879422591338 4.034736482094483 2.98701630458123 2.8922101276690353
user_002 Jogging 1.446034902895e12 -6.28393 -1.49389 1.49389 -12.14694 -4.357465454545455 -3.3414327272727267 39.4877762449 2.2317073320999996 2.2317073320999996 6.6295694361775865 13.545898291325244 5.863010000000001 2.863575454545455 4.835322727272727 3.6717825619834716 4.083489504132231 2.464850578512396 34.37488626010001 8.20006438387521 23.380345876880163 17.17902520682983 17.189657202903156 8.621513752262207 4.144758763405879 4.14604114824047 2.9362414328972006
user_002 Jogging 1.446034903033e12 -2.60518 -5.2876 1.49389 3.620127363636364 -2.727110272727273 -1.8957118181818187 6.7869628323999995 27.958713760000002 2.2317073320999996 6.080903216176032 6.2024957720086515 6.225307363636364 2.5604897272727274 3.3896018181818186 4.484111008264463 2.532939611570248 2.103498991735538 38.75445177174513 6.556107643469166 11.489400485821491 24.000768885446554 7.253680017838164 5.325640246205652 4.89905795898013 2.693265679029487 2.307734873464812
user_002 Jogging 1.446034903138e12 -12.41518 -11.72542 -7.7239e-2 -12.181777272727272 -11.728901818181818 0.26764363636363636 154.1366944324 137.4854741764 5.965863121e-3 17.07712313218831 17.103313548749245 0.23340272727272726 3.4818181818181415e-3 0.34488263636363636 5.954216669421488 3.747789917355372 1.2268833388429752 5.4476833098347104e-2 1.2123057851239389e-5 0.11894403286513223 41.42377563739363 22.08025245799609 2.545374521742775 6.4361304863554185 4.698962913026245 1.595422991479932
user_002 Jogging 1.446034903162e12 -15.82569 -12.79839 -0.345482 -13.836517272727274 -12.927282727272729 0.260676 250.4524639761 163.7987865921 0.119357812324 20.35609511621824 19.101228338167484 1.9891727272727255 0.1288927272727296 0.606158 4.112941603305784 2.917411074380166 1.1961640578512398 3.956808138925613 1.6613335143802255e-2 0.36742752096399994 25.41021847834294 18.272074295056942 2.3195890725029122 5.040854935260778 4.274584692699039 1.5230197216395172
user_002 Jogging 1.446034903332e12 -3.90807 2.68302 -4.59904 -3.5248700000000004 -3.507452363636365 -2.418262727272727 15.2730111249 7.1985963204 21.151168921599997 6.604754073158213 6.2858962299151155 0.38319999999999954 6.190472363636365 2.1807772727272727 4.531614380165291 4.087922247933886 1.003929388429752 0.14684223999999965 38.3219480849456 4.755789513243801 26.03798165480255 17.937086675501124 1.3010746092393464 5.1027425620741 4.23521979069577 1.1406465750789534
user_002 Jogging 1.446034903364e12 -3.06503 3.90927 -2.52974 -2.817686363636364 0.32109581818181826 -3.007001818181818 9.3944089009 15.282391932899998 6.3995844675999995 5.574619745005035 5.520307117261362 0.24734363636363632 3.5881741818181814 0.47726181818181823 2.2561485950413216 4.613006 1.049850388429752 6.117887444958676e-2 12.874993959066575 0.22777884309421492 10.156513458621633 22.844478304031163 1.672854066725234 3.186928530516747 4.779589763152394 1.2933885984982372
user_002 Jogging 1.446034903559e12 -19.58108 -10.42253 -8.81427 -15.08018545454545 -16.330821818181818 -7.13166 383.4186939664 108.6291316009 77.69135563290001 23.86920989895141 23.72028927423204 4.50089454545455 5.908291818181818 1.6826100000000004 5.996020479338842 5.813287438016529 3.578356950413223 20.258051709302517 34.90791220879421 2.8311764121000014 37.15895341889142 43.90340861610187 14.47403434508205 6.095814418015974 6.625964730973284 3.80447556768105
user_002 Jogging 1.446034903656e12 -3.02671 -2.10702 1.83878 -12.244483636363638 -4.859112727272729 -3.811728818181818 9.1609734241 4.439533280399999 3.3811118884000004 4.120875949710206 13.973353179277263 9.217773636363638 2.752092727272729 5.650508818181818 5.437367190082646 4.621873553719009 3.1761519338842983 84.96735081124054 7.574014379507447 31.928249904350483 40.0247632765042 23.596950291099475 14.544418632169284 6.326512726337015 4.857669224134089 3.81371454518679
user_002 Jogging 1.446034903664e12 -1.91542 -1.37893 2.98839 -10.638514545454544 -4.179798181818182 -2.759661545454545 3.6688337763999996 1.9014479449 8.9304747921 3.8079858867122915 12.21590272555592 8.723094545454545 2.8008681818181818 5.748051545454545 5.953899504132232 4.342230082644629 3.610976867768595 76.09237844893885 7.844862571921487 33.04009656920238 46.1014217529465 21.170256110268816 17.46341094419858 6.789802777175969 4.6011146595437955 4.178924615759248
user_002 Jogging 1.446034903688e12 1.68669 0.767005 1.8771 -5.3433436363636355 -2.4519013636363636 -0.11207609090909067 2.8449231561 0.5882966700250001 3.52350441 2.637560281040985 7.330031668983031 7.030033636363635 3.2189063636363637 1.9891760909090908 7.687181198347106 3.4079735454545457 4.361865388429752 49.42137292840412 10.361358177858678 3.9568215206443713 62.03217093976252 12.505821022904898 21.370784418181128 7.876050465795818 3.5363570270696507 4.622854574630391
user_002 Jogging 1.446034903802e12 -8.81307 -2.91174 -1.61005 -0.5846565454545452 -0.9922438181818181 -2.317236909090909 77.6702028249 8.4782298276 2.5922610025 9.420227898251719 6.299631258550062 8.228413454545455 1.919496181818182 0.7071869090909091 4.653226421487603 2.1057176611570245 1.7256828016528922 67.70678797894467 3.684465592014579 0.5001133243895537 30.638221487023472 5.665971506206171 4.285349532874221 5.535180348193134 2.38033012546709 2.0701085799721284
user_002 Jogging 1.446034903891e12 -14.79104 -15.78737 2.56686 -12.119069090909091 -13.000438181818181 1.3022913636363636 218.77486428160003 249.24105151689997 6.5887702596 21.785423706187125 18.60925747454722 2.671970909090909 2.7869318181818183 1.2645686363636366 4.556316016528926 5.576081132231405 3.255326991735537 7.1394285390281 7.766988959194216 1.5991338360745873 23.245656366794588 43.7177504637925 17.94761159847474 4.821374945676242 6.61193999245248 4.236462155912022
user_002 Jogging 1.446034904036e12 -4.5212 -3.86975 -2.72134 -8.691145454545454 -7.99092909090909 -1.2721353636363635 20.441249440000004 14.974965062499999 7.405691395600001 6.543844886463921 12.128840394525708 4.169945454545454 4.121179090909091 1.4492046363636366 3.656264380165289 2.8268364462809914 1.3494450743801654 17.388445093884293 16.984117099346278 2.1001940780578603 14.260647954712015 10.580754409606984 2.6915586961146896 3.776327310325737 3.2528071583798175 1.6405970547683821
user_002 Jogging 1.446034904052e12 -2.4519 -2.4519 -1.34181 -7.266326363636364 -6.377991818181818 -1.7737833636363638 6.011813610000001 6.011813610000001 1.8004540760999999 3.7180749449278188 10.010471067635713 4.814426363636364 3.926091818181818 0.43197336363636385 3.708519669421487 3.345269421487602 1.1705110743801652 23.17870121087686 15.414196964794213 0.18660098689131424 14.723721494830494 13.114459041074072 2.413511653743653 3.8371501788215814 3.62138910379347 1.5535480854301398
user_002 Jogging 1.446034904068e12 -3.06503 1.03525 -1.03525 -6.00524 -4.249472 -1.9235813636363637 9.3944089009 1.0717425625 1.0717425625 3.3967475658193975 7.858612444492149 2.9402099999999995 5.284722 0.8883313636363637 3.514700991735537 4.132577867768595 1.2607692396694217 8.644834844099996 27.928286617284005 0.7891326116200413 13.18482379751194 17.94021551195684 2.50944098331362 3.6310912681330305 4.235589157597422 1.584121517849442
user_002 Jogging 1.446034904141e12 -4.98104 -1.03405 0.459245 -4.110125454545455 2.7248261818181816 -2.1918236363636363 24.8107594816 1.0692594024999997 0.210905970025 5.107927647698722 6.009845601241079 0.8709145454545455 3.7588761818181817 2.6510686363636364 2.47118347107438 4.154430181818182 1.6769083719008264 0.7584921454842976 14.129150150240033 7.028164914710951 7.068442432986174 20.290694168959366 3.8194279934045157 2.658654252246082 4.504519304982427 1.9543356910736998
user_002 Jogging 1.44603490419e12 -0.842448 -2.18366 1.30229 -3.5527377272727274 -0.22583909090909077 -0.26884136363636374 0.7097186327039999 4.768370995600001 1.6959592440999998 2.6784415006499582 5.301884437122247 2.7102897272727273 1.9578209090909093 1.5711313636363637 2.3647737520661156 3.229358115702479 2.469601165289256 7.345670405760075 3.8330627120735548 2.46845376180186 6.257878597314694 12.208151199119698 6.884548005580183 2.5015752231973147 3.4940164852386855 2.623842221929547
user_002 Jogging 1.44603490423e12 -9.2346 -13.33487 -3.87095 -2.5668612727272726 -4.789440909090909 -0.23748899999999998 85.27783716 177.8187579169 14.9842539025 16.675756324059186 5.879288130861806 6.667738727272727 8.545429090909092 3.633461 2.5617600909090905 4.247855041322314 2.637450396694215 44.45873973517253 73.0243583477554 13.202038838521 8.912440530990839 21.106037928951018 7.913980677297903 2.985371087652394 4.594130813217123 2.813179816026324
user_002 Jogging 1.446034904247e12 -11.4955 -11.95534 -4.94392 -4.120576727272727 -6.674103636363637 -1.198980909090909 132.14652025 142.93015451559998 24.442344966400004 17.306617801638772 8.42209099464779 7.374923272727273 5.281236363636363 3.7449390909090914 3.597359198347107 4.569618677685951 2.868639413223141 54.389493278614346 27.89145752859503 14.024568794619011 18.159871432887243 25.35676770577446 9.372191101671767 4.26144006562186 5.035550387571796 3.061403452939806
user_002 Jogging 1.446034904433e12 -4.48288 -1.80046 1.45557 -9.56206 -3.9951645454545455 -3.5992239999999995 20.0962130944 3.2416562115999996 2.1186840249000003 5.045448773984332 11.195118393459259 5.079180000000001 2.1947045454545453 5.054793999999999 5.569430082644629 2.9224779338842977 3.0064033553719 25.79806947240001 4.816728041838842 25.550942382435995 33.99202304405725 8.910876950714426 11.493034828647646 5.830267836391159 2.9851092024772603 3.390137877527645
user_002 Jogging 1.446034904538e12 2.72134 -2.6435 -3.41111 3.4424599090909087 -0.6090423636363635 -1.4950904545454546 7.405691395600001 6.98809225 11.635671432099999 5.101907004023103 4.55478708374157 0.7211199090909086 2.034457636363636 1.9160195454545452 4.419503983471075 1.9660537438016528 2.015458099173554 0.5200139232872804 4.139017874158314 3.6711308985638422 22.016640849837806 4.48710159313118 4.649995244198693 4.692189345053949 2.1182779782481758 2.1563847625594774
user_002 Jogging 1.446034904684e12 -12.22358 -12.76007 -0.767005 -8.001378818181818 -5.799704 -0.22703663636363636 149.4159080164 162.81938640490003 0.5882966700250001 17.686819699746053 10.153678420593193 4.222201181818182 6.9603660000000005 0.5399683636363637 6.781428462809917 3.266728289256198 1.2351171652892563 17.826982819746853 48.446694853956004 0.2915658337281323 48.622979422365624 18.36825048902798 2.086747875931804 6.973017956549777 4.285819698614021 1.44455802096413
user_002 Jogging 1.446034904692e12 -12.6451 -12.30022 -0.920286 -9.081314545454545 -6.775130363636364 -0.1573635454545455 159.89855400999997 151.29541204839998 0.8469263217960001 17.664679232304106 11.538779339376402 3.563785454545455 5.525089636363636 0.7629224545454545 6.725056115702478 3.691418768595042 1.289588834710744 12.700566766029754 30.526615489852855 0.5820506716496611 48.18622526434305 21.077174385491052 2.1372244049430615 6.94162987088357 4.59098838873407 1.4619248971623207
user_002 Jogging 1.446034904756e12 -14.06296 -10.57581 -0.690364 -14.644726363636364 -12.767033636363635 -0.25839 197.76684396160002 111.84775715610002 0.476602452496 17.609406678539628 19.475279502295486 0.5817663636363637 2.1912236363636346 0.43197399999999997 3.2382232727272733 4.010647933884297 0.4766286280991736 0.33845210185867775 4.8014610245586695 0.18660153667599996 12.985092626615568 20.309954201626507 0.2758041644698933 3.603483401739984 4.506656654508585 0.5251706051083718
user_002 Jogging 1.446034904846e12 -5.86241 0.881966 -2.22318 -8.245237272727273 -6.050527636363636 -2.007189090909091 34.3678510081 0.7778640251560001 4.9425293124000005 6.331527805013257 10.729046543855477 2.3828272727272735 6.9324936363636365 0.21599090909090934 4.018248099173554 3.8266475206611585 0.9485068347107437 5.677865811652896 48.05946801822232 4.665207280991746e-2 18.196603209903987 16.717464723465596 1.2873520720054776 4.265747673023334 4.08869963722766 1.134615385055869
user_002 Jogging 1.446034904854e12 -5.36425 3.14286 -2.52974 -7.541537272727272 -4.8382130909090915 -2.0594445454545456 28.7751780625 9.877568979600001 6.3995844675999995 6.712103359581109 9.819530956042142 2.1772872727272716 7.981073090909092 0.4702954545454543 4.071453140495868 4.330194743801655 0.856348520661157 4.74057986798016 63.69752768243321 0.22117781456611546 18.397149987892792 21.966001243425268 1.1072440962802064 4.289189898791238 4.686790078873308 1.0522566684417858
user_002 Jogging 1.446034904878e12 -2.10702 4.5224 -4.36911 -5.378180909090909 -1.4207367272727274 -2.4983863636363637 4.439533280399999 20.45210176 19.0891221921 6.631798943914087 7.87933259704107 3.271160909090909 5.943136727272727 1.8707236363636364 3.951109338842975 5.189711123966943 0.8959354462809919 10.70049369316446 35.320874159057986 3.4996069236495866 17.659479898589257 31.220205179266724 1.239098651056581 4.20231839567033 5.587504378456157 1.1131480813694918
user_002 Jogging 1.44603490491e12 -1.34061 -1.11069 0.497565 -3.281014181818182 1.4567706363636361 -2.52974 1.7972351721000002 1.2336322760999998 0.24757092922499999 1.810645845389153 5.179318167006664 1.940404181818182 2.567460636363636 3.0273049999999997 2.96301573553719 4.889799148760331 1.2677373636363638 3.7651683888174885 6.591854119276767 9.164575563024998 9.386070086848262 30.130454763090782 2.3786902039375906 3.0636693827579147 5.489121492833874 1.5423002962904437
user_002 Jogging 1.446034904918e12 -1.30229 -2.03038 1.53221 -2.9361314545454547 1.5821824545454546 -2.1813736363636362 1.6959592440999998 4.1224429444 2.3476674841 2.857633579135016 4.84376388010314 1.6338414545454547 3.6125624545454547 3.7135836363636363 2.677355123966942 4.804924578512398 1.5457965702479337 2.669437898591207 13.05060748799148 13.790703424267768 7.55499995359014 29.43798477202156 3.5933962969675406 2.748636016934607 5.425678277600097 1.8956255687681416
user_002 Jogging 1.446034905008e12 -14.40784 -15.86401 -3.67935 -4.430622363636363 -7.21407090909091 -0.7252006363636364 207.5858534656 251.6668132801 13.5376164225 21.74374124129056 8.775807580478014 9.977217636363637 8.64993909090909 2.9541493636363634 2.9516145867768597 5.136505157024794 1.7073115454545453 99.54487176336559 74.82144627643717 8.72699846267313 19.804817630125125 33.486343327562736 4.005089556027638 4.450260400260318 5.786738574323428 2.0012719845207543
user_002 Jogging 1.446034905072e12 -17.51178 -12.83671 -9.88724 -16.44578272727273 -14.568086363636365 -6.950508181818182 306.6624387684001 164.7811236241 97.75751481760001 23.857935309035025 23.287859721835208 1.065997272727273 1.7313763636363646 2.9367318181818183 7.326463776859504 4.696928760330579 3.9678935537190085 1.1363501854619842 2.997664112558681 8.624393771921488 63.111678662534125 30.135037766228844 17.07495917870299 7.94428591268807 5.489538939312558 4.132185762850333
user_002 Jogging 1.44603490508e12 -17.24354 -10.95901 -8.69931 -17.327149999999996 -14.338164545454545 -7.570600909090908 297.3396717316 120.09990018009998 75.67799447610001 22.20625061526146 23.891116942422705 8.360999999999663e-2 3.3791545454545453 1.1287090909090924 6.854269198347108 4.205415454545455 3.891886876033058 6.990632099999437e-3 11.418685442066115 1.27398421190083 60.58007336537378 24.155800296036443 16.839833156973718 7.7833202019044405 4.914855063583914 4.103636577107397
user_002 Jogging 1.446034905177e12 -5.47921 0.345482 2.2603 -12.596334545454546 -2.800267454545455 -3.7943080000000005 30.021742224100002 0.119357812324 5.1089560899999995 5.937175770214656 13.939753347675527 7.117124545454546 3.145749454545455 6.054608 3.6648138842975198 5.536176719008265 3.1514500495867774 50.653461795511575 9.895739630773027 36.658278033664 18.033930212002403 31.976428244376894 13.719504742224348 4.246637518319924 5.654770397140532 3.703984981371327
user_002 Jogging 1.446034905234e12 5.97857 1.83997 -2.6447 -1.852711727272727 1.1327883636363636 0.6821992727272729 35.7432992449 3.3854896009 6.994438089999999 6.791408317558296 6.010528689599741 7.831281727272727 0.7071816363636365 3.326899272727273 7.4420579008264465 2.783447090909091 4.073986148760331 61.32897349191571 0.5001058668099506 11.068258770873257 57.684432289683144 10.435126585578507 19.986831797446357 7.595026812966703 3.230344654302155 4.470663462781151
user_002 Jogging 1.446034905339e12 -5.47921 -3.52487 -4.59904 -1.4451221818181816 -3.3228180909090907 -1.2372999999999998 30.021742224100002 12.424708516899999 21.151168921599997 7.97481157536653 6.509562618986421 4.034087818181819 0.2020519090909092 3.3617399999999997 5.088052165289255 2.322020347107438 1.70287826446281 16.273864524802946 4.0824973967281034e-2 11.301295827599999 31.004942615609924 7.3387421684781975 4.120292266177289 5.568208205123971 2.70901128983956 2.0298503063470688
user_002 Jogging 1.446034905355e12 -5.63249 -2.95007 -4.75232 -3.6328649090909084 -3.6398318181818183 -2.097765272727273 31.724943600099998 8.702913004900001 22.5845453824 7.938035146520832 6.782794744382937 1.9996250909090914 0.6897618181818181 2.654554727272727 4.8840994710743795 2.0626460743801656 2.206426214876033 3.998500504193192 0.47577136582148755 7.0466608000859825 29.68185233968346 6.288701452326577 6.453050962520794 5.448105389920744 2.5077283450020214 2.540285606486167
user_002 Jogging 1.446034905469e12 -15.55745 -16.05561 1.76214 -14.630792727272727 -14.028118181818183 3.1346995454545454 242.0342505025 257.7826124721 3.1051373796000004 22.425922508432066 21.330167876689657 0.9266572727272724 2.0274918181818187 1.3725595454545454 4.255771157024793 3.5739233057851227 5.2546326280991735 0.8586937010983465 4.110723072794217 1.8839197058183883 27.394483158568065 25.26332975107513 37.281628055188655 5.233973935602666 5.026263995362274 6.105868329336022
user_002 Jogging 1.446034905615e12 -3.67815 2.60638 -1.64837 -6.73681 -4.211151818181819 -2.275431818181818 13.5287874225 6.793216704400001 2.7171236568999997 4.7999091432859435 8.70367169629476 3.05866 6.81753181818182 0.6270618181818182 4.062901983471075 4.511978595041322 1.0020288842975207 9.3554009956 46.47874009192151 0.3932065238214876 17.284075030573106 22.3073486315281 1.8275789039897425 4.157412059271141 4.72306559678437 1.3518797668393971
user_002 Jogging 1.446034905647e12 -1.30229 3.25783 -5.36544 -3.6154460909090913 -0.4418272727272725 -2.857203636363636 1.6959592440999998 10.613456308899998 28.787946393600006 6.410722420024127 6.502811399641062 2.313156090909091 3.699657272727272 2.5082363636363643 3.985945512396695 4.648158429752066 0.9136700826446282 5.3506911009098275 13.687463935643796 6.291249655867772 16.803033608622233 24.367466543648614 1.6582827814492298 4.099150352039095 4.936341412792334 1.2877432901977124
user_002 Jogging 1.446034905727e12 1.07357 -6.70546 1.53221 -1.8213575454545456 -2.3613268181818183 0.4035049090909093 1.1525525448999998 44.96319381160001 2.3476674841 6.96156690987022 5.193493556753845 2.8949275454545456 4.344133181818182 1.1287050909090908 1.1024227851239672 3.1625355371900823 3.0599230743801655 8.38060549343148 18.871493101373762 1.2739751822440988 1.9395304452291355 11.662849426100301 12.069842032723182 1.3926702571783227 3.4150914228026608 3.474167818733456
user_002 Jogging 1.446034905857e12 -17.20522 -5.82409 -6.20849 -18.59172 -10.513101818181818 -8.033929090909092 296.01959524840004 33.9200243281 38.545348080100005 19.195962274827487 22.924337680223914 1.386499999999998 4.689011818181818 1.825439090909092 6.054610214876033 2.2665984297520656 3.3813718842975207 1.9223822499999947 21.98683183104876 3.3322278746190124 54.52274721195797 7.463359831681368 14.768475546288306 7.383952004987435 2.7319150484012797 3.842977432445877
user_002 Jogging 1.446034905874e12 -14.21624 -3.90807 -6.55337 -18.072653636363636 -8.962870909090908 -8.103602727272728 202.10147973760002 15.2730111249 42.9466583569 16.134470837910985 21.862878092852522 3.8564136363636354 5.054800909090908 1.5502327272727277 4.436605834710743 2.4822690909090905 2.7169417520661163 14.871926134731398 25.551012230546267 2.403221508707439 30.28166977085812 9.45894439590338 10.4348205853482 5.50287831692271 3.0755396918107527 3.230297290552094
user_002 Jogging 1.446034906043e12 4.79064 -6.43721 -3.52607 5.079782727272728 -0.9121207272727273 -0.6102407272727273 22.9502316096 41.43767258410001 12.4331696449 8.764763193526681 6.032297508238341 0.2891427272727283 5.525089272727273 2.9158292727272723 4.460991074380165 2.1611383471074377 1.8317732727272726 8.360351673471132e-2 30.52661147160599 8.502060347693254 26.557241211071098 7.379857479956052 4.511605649858295 5.1533718293046835 2.7165893101379996 2.1240540600131377
user_002 Jogging 1.4460349061e12 -8.69811 -6.62882 -5.67201 -2.187142090909091 -5.298055454545454 -2.2510471818181816 75.65711757209999 43.9412545924 32.171697440100004 12.31949956794512 9.109836937026863 6.510967909090908 1.3307645454545458 3.4209628181818186 5.894360165289256 3.051057355371901 1.7427830826446282 42.39270311321163 1.770934275438844 11.70298660338249 49.28009459437685 11.136380565774072 4.236912042945018 7.019978247429036 3.337121598889389 2.0583760693675535
user_002 Jogging 1.446034906132e12 -15.74905 -17.81835 0.344284 -8.572700272727273 -9.20672818181818 -1.6274719090909096 248.0325759025 317.49359672249994 0.11853147265599999 23.78328623419514 13.337573546264622 7.1763497272727275 8.611621818181819 1.9717559090909096 7.523449586776858 4.22220267768595 1.909365611570248 51.49999540812735 74.16003033938513 3.8878213650349194 61.7491867891929 25.090541422510398 5.45840222276125 7.858065079215932 5.009045959313051 2.336322371326622
user_002 Jogging 1.446034906319e12 -3.56319 -4.98104 -1.22685 -7.67043181818182 -8.49606 -1.3487758181818184 12.696322976100001 24.8107594816 1.5051609225 6.2459781764108016 11.641939368073643 4.107241818181819 3.51502 0.12192581818181836 5.061765454545454 2.8714898347107436 0.936471603305785 16.869435353021498 12.355365600399999 1.4865905139305828e-2 26.613912440978808 10.115667026524044 1.3641360147597592 5.158867360281596 3.1805136419333344 1.1679623344781969
user_002 Jogging 1.446034906366e12 -3.60151 4.33079 -5.67201 -4.806859090909091 -2.3578414545454547 -2.4461315454545454 12.970874280100002 18.7557420241 32.171697440100004 7.993642082574126 7.147612929840088 1.205349090909091 6.688631454545455 3.225878454545455 2.907910165289256 5.069999818181818 0.8607821404958678 1.452866430955372 44.737790734734844 10.406291803500572 11.57677391751818 27.53574990156487 1.5309432143551114 3.402465858391261 5.247451753143126 1.237312900747063
user_002 Jogging 1.446034906408e12 -3.37159 -2.6435 -0.537083 -3.883689090909091 0.8924172727272727 -3.6201266363636364 11.3676191281 6.98809225 0.28845814888899995 4.3178894760043365 6.298627808131697 0.512099090909091 3.5359172727272727 3.0830436363636364 1.0894361157024794 4.591786280991736 1.653474876033058 0.26224547890991745 12.502710959571074 9.505158063722314 1.5332669035144262 25.43087279685827 3.9924662865406377 1.2382515509840584 5.042903211133273 1.9981156839734375
user_002 Jogging 1.446034906432e12 -0.919089 -6.01569 1.22565 -3.0406417272727277 -1.6819454545454447e-2 -2.571543909090909 0.8447245899210001 36.188526176100005 1.5022179224999999 6.207694313392132 6.2486913175856165 2.1215527272727277 5.998870545454546 3.797193909090909 1.1369413223140497 4.950603520661157 2.6136990661157027 4.500985974598349 35.98644782112212 14.418681583237097 1.6017300063233662 28.800501000828568 8.60560462482137 1.2655947243582228 5.366609823792723 2.9335310846864004
user_002 Jogging 1.44603490644e12 -0.535886 -4.44456 1.14901 -2.6713731818181823 -0.6369121818181819 -2.2440793636363634 0.287173804996 19.7541135936 1.3202239801000002 4.621851509806 6.148168785920205 2.135487181818182 3.807647818181818 3.3930893636363635 1.2534859421487603 4.643724429752066 2.887324933884298 4.560305503709762 14.49818190730476 11.513055429622222 1.950079957320572 25.427603458128235 9.638896397270868 1.3964526333966978 5.0425790482776005 3.1046572109124813
user_002 Jogging 1.446034906586e12 -18.73803 -8.77475 -10.577 -17.306248181818184 -11.910050909090911 -9.437845454545455 351.11376828089993 76.99623756249999 111.872929 23.237532890636217 23.287164041305836 1.4317818181818147 3.135300909090912 1.139154545454545 7.446174330578511 3.08209305785124 5.358825710743801 2.049999174876023 9.8301117905463 1.2976730784297512 71.52977110671443 15.74948846692201 31.739869182092267 8.457527481877575 3.968562518963511 5.633814798348652
user_002 Jogging 1.44603490665e12 -11.84038 -1.8771 -5.05888 -16.773248181818182 -5.029813636363637 -8.096633636363636 140.19459854439998 3.52350441 25.592266854400002 13.011931824629269 19.655628983671996 4.932868181818183 3.152713636363637 3.037753636363636 1.9451499999999997 4.46225694214876 2.7549444214876035 24.333188499194225 9.939603272913228 9.227947155240493 5.12739384022141 23.162048677438687 8.607126122767712 2.2643749336674373 4.812696611821556 2.933790401983024
user_002 Jogging 1.446034906675e12 -7.28026 -0.612526 -1.95493 -14.35906818181818 -2.295136727272727 -5.773029999999999 53.0021856676 0.375188100676 3.8217513049000003 7.563010318198436 15.684182358959674 7.0788081818181805 1.6826107272727273 3.8180999999999994 3.3383008264462815 4.440089074380165 2.8638885950413226 50.109525274976015 2.8311788595332565 14.577887609999996 16.27907204168686 22.948845464150352 8.696309456470926 4.034733205763035 4.790495325553544 2.9489505686720023
user_002 Jogging 1.446034906691e12 -3.56319 -0.267643 -0.575403 -11.673162727272727 -1.3859 -4.44575390909091 12.696322976100001 7.163277544900001e-2 0.331088612409 3.6192601956695514 12.589850897609228 8.109972727272726 1.1182569999999998 3.87035090909091 4.516729669421488 3.7012356942148754 3.247091570247935 65.77165763710742 1.2504987180489997 14.979616159500832 26.88297084850962 17.91654209487913 10.707331798979867 5.184879058233626 4.232793651346488 3.2722059530200522
user_002 Jogging 1.446034906796e12 3.48775 -1.8771 -0.15388 4.167061818181818 -0.2641598181818182 -1.0526639999999998 12.1644000625 3.52350441 2.3679054399999996e-2 3.9637839909485484 4.577401749353625 0.6793118181818176 1.6129401818181819 0.8987839999999998 4.622822 1.3089080247933884 0.7635545371900826 0.46146454632148687 2.6015760301236694 0.8078126786559997 29.624850336280137 2.1701642934302128 0.9407629565015231 5.4428715156872975 1.473147750033992 0.9699293564489752
user_002 Jogging 1.446034906901e12 -13.90968 -14.82936 0.574206 -9.422715454545456 -7.56243818181818 -1.536894909090909 193.4791977024 219.90991800959998 0.329712530436 20.34007935683723 12.62745717317743 4.486964545454544 7.266921818181819 2.1111009090909088 5.990321280991736 3.6831837438016533 1.5651153305785124 20.132850832166103 52.808152711566954 4.456747048364462 39.355071607140815 25.29494812891069 3.5116251320448835 6.27336206568223 5.029408327915988 1.8739330649852153
user_002 Jogging 1.446034906942e12 -13.25823 -11.95534 0.957409 -12.234032727272727 -11.370082727272724 6.907418181818191e-2 175.78066273289997 142.93015451559998 0.9166319932809999 17.878127677186473 17.14557775538888 1.0241972727272728 0.5852572727272758 0.888334818181818 3.535603636363635 4.105973884297521 2.7207424297520664 1.0489800534619835 0.3425260752801689 0.7891387491941237 14.143379773647181 27.92088436341037 9.16121299243646 3.7607685083832507 5.284021608908348 3.0267495754416913
user_002 Jogging 1.446034906982e12 -18.20155 -13.83303 0.114362 -14.93735727272727 -13.091012727272728 0.9992131818181815 331.2964224025 191.35271898090002 1.3078667044000002e-2 22.861807016297817 20.021431218737533 3.2641927272727305 0.7420172727272725 0.8848511818181816 2.679888842975208 2.0886154545454545 2.392960826446281 10.654954160780186 0.5505896330256195 0.7829616139650326 8.170243855914727 9.0530824903009 7.778509837779979 2.8583638424656033 3.008834074903583 2.7889979988841835
user_002 Jogging 1.446034907039e12 -10.49917 -9.08132 -1.49509 -15.240435454545455 -12.43260181818182 -0.7321686363636364 110.23257068889998 82.47037294239999 2.2352941081 13.962028424960321 19.741622779485223 4.741265454545456 3.3512818181818194 0.7629213636363636 2.6935066115702493 1.4317850413223132 1.1613272644628099 22.479598110466128 11.23108982487604 0.5820490070927686 8.706909684042682 2.7814735594394424 2.090464572249903 2.9507473094188668 1.6677750326226384 1.4458438962245899
user_002 Jogging 1.44603490712e12 -3.06503 0.11556 -2.33814 -5.9286 -3.9533609090909083 -2.0037054545454542 9.3944089009 1.3354113599999998e-2 5.466898659600001 3.8567682940643455 7.647626963046448 2.86357 4.068920909090909 0.3344345454545459 4.9176669421487595 4.3891014049586765 0.6926151570247933 8.2000331449 16.556117364437185 0.11184646519338871 24.717201992823444 19.88589517058234 0.711008412292816 4.971639769012176 4.459360399270543 0.8432131476043385
user_002 Jogging 1.446034907209e12 -2.60518 -2.91174 -0.268841 -3.305399090909091 1.7563679090909092 -2.2754321818181817 6.7869628323999995 8.4782298276 7.2275483281e-2 3.9163079734976156 5.2126819531418045 0.7002190909090911 4.668107909090909 2.0065911818181816 0.514316033057851 3.7867450082644627 1.3510296363636363 0.49030677527355393 21.7912314509171 4.026408170950487 0.3872811612404208 17.10425060984232 2.3858715021441905 0.6223191795537245 4.135728546440436 1.5446266546140497
user_002 Jogging 1.446034907257e12 -4.9044 -8.73643 -1.03525 -3.1416672727272728 -3.047608181818182 -0.3977359999999999 24.05313936 76.3252091449 1.0717425625 10.072243596508178 5.088328791502168 1.7627327272727271 5.688821818181818 0.6375140000000001 0.4753612396694214 3.6527827355371896 1.6974960330578512 3.1072266677983467 32.36269367902149 0.40642410019600017 0.44791110553456037 15.898295291524887 4.0854805384043535 0.6692616121776 3.9872666441467 2.0212571678053126
user_002 Jogging 1.44603490729e12 -14.5228 -14.98264 -4.714 -6.297867272727273 -8.168595454545455 -1.5194766363636367 210.91171984000002 224.4795013696 22.221796000000005 21.39189138925308 10.659201066417712 8.224932727272726 6.814044545454545 3.194523363636364 2.833486611570248 5.709093859504131 2.4113304049586772 67.64951836816196 46.43120306743883 10.204979520818588 18.223977300926823 37.259208245871726 7.400173065667297 4.268955059604964 6.104032130147393 2.720325911663398
user_002 Jogging 1.446034907403e12 -16.32385 -2.98839 -6.70665 -18.60913818181818 -8.074537272727271 -9.162636363636363 266.4680788225 8.9304747921 44.9791542225 17.899097961548232 22.465247190479637 2.2852881818181814 5.086147272727271 2.455986363636363 2.8151174380165287 3.4934809917355367 3.2850951074380172 5.222542073957849 25.868894079871062 6.0318690183677655 13.08808219941119 15.12350955082885 15.124677542114034 3.6177454580734656 3.888895672402237 3.8890458395490834
user_002 Jogging 1.446034907476e12 -1.72382 -1.8771 7.6042e-2 -9.690955454545456 -2.1314045454545454 -3.644511272727273 2.9715553923999996 3.52350441 5.782385764e-3 2.5496749181344667 10.660497360124252 7.967135454545456 0.2543045454545454 3.720553272727273 5.511791239669422 2.9132938842975205 2.9712496363636363 63.47524735107523 6.467080183884294e-2 13.842516655201623 34.147024354188275 11.661232288066863 9.041529347618932 5.843545529401502 3.4148546510893936 3.0069135916449166
user_002 Jogging 1.446034907508e12 3.90927 -1.18733 0.689167 -3.514419181818181 -1.7725872727272725 -0.8575789090909095 15.282391932899998 1.4097525289 0.47495115388899994 4.143319395809234 5.937236157961707 7.423689181818181 0.5852572727272725 1.5467459090909095 7.149745727272728 1.24398520661157 3.22270714876033 55.1111610682443 0.342526075280165 2.392422907289464 51.78529644795792 2.918500147336363 10.751469564364557 7.196200139515153 1.708361831503023 3.278943360957087
user_002 Jogging 1.44603490771e12 -17.43514 -8.54483 3.48655 -12.686907272727273 -8.206916181818181 0.26067618181818175 303.9841068196 73.01411972889998 12.1560309025 19.726993117325307 16.107928203941583 4.748232727272727 0.33791381818181776 3.2258738181818183 5.759764016528926 4.008115272727272 3.1717190578512398 22.5457140323438 0.11418574851821459 10.406261890830942 35.661160756290485 30.533416247583013 12.024295610812407 5.971696639673727 5.525705045293588 3.4676066113116706
user_002 Jogging 1.446034907759e12 -15.86401 -13.71807 0.919089 -16.041677272727274 -11.666194545454545 0.6682655454545454 251.6668132801 188.18544452490002 0.8447245899210001 20.992784055358666 20.2523659330661 0.17766727272727323 2.0518754545454563 0.2508234545454546 3.3924554545454555 2.6558187107438016 2.6403015702479338 3.156565979834729e-2 4.210192880966122 6.291240535011575e-2 22.638652582823227 12.02031983930934 9.005259334218808 4.758009308820573 3.4670332907702717 3.000876427682221
user_002 Jogging 1.446034907783e12 -15.05928 -13.10495 -0.767005 -15.623637272727272 -12.209646363636363 -3.1951000000000035e-2 226.78191411839998 171.73971450250002 0.5882966700250001 19.977735739841116 20.14726044376983 0.564357272727273 0.8953036363636375 0.735054 1.4406541322314053 1.6569572396694214 1.9061984958677685 0.3184991312801656 0.8015686012859525 0.540304382916 6.287423676600526 3.4110413267804827 6.197944188322239 2.5074735644868773 1.8469004647734764 2.489567068452312
user_002 Jogging 1.446034907864e12 -6.20729 -2.56686 -1.38013 -12.718260000000003 -7.496248181818183 -2.3799413636363638 38.530449144100004 6.5887702596 1.9047588169000003 6.857403168882518 15.077684317245383 6.510970000000002 4.929388181818183 0.9998113636363637 2.894924958677685 3.608126859504132 1.1971138512396695 42.39273034090003 24.298867847048772 0.9996227628564051 11.904642383664612 15.582626079113071 2.082914951146491 3.4503104764157984 3.947483512202815 1.443230733855987
user_002 Jogging 1.446034907913e12 -3.63983 4.56072 -1.34181 -6.733325454545454 -1.8318086363636361 -2.6168318181818178 13.248362428899998 20.8001669184 1.8004540760999999 5.987402059608157 8.085788948485714 3.0934954545454545 6.392528636363636 1.2750218181818178 4.686161570247934 4.656393636363637 1.0932376942148758 9.569714127293388 40.86442236672913 1.6256806368396686 23.52487566892179 22.36712104831754 1.8064930810530717 4.850244908138329 4.729389077705231 1.3440584366213664
user_002 Jogging 1.446034907945e12 -3.06503 1.49509 -3.25783 -4.030002727272727 1.2512349999999997 -2.5645781818181814 9.3944089009 2.2352941081 10.613456308899998 4.7162653994341746 5.7354608954132 0.9649727272727269 0.24385500000000038 0.6932518181818184 3.8944193388429755 4.135427107438016 0.7736911983471072 0.9311723643801645 5.946526102500018e-2 0.48059808341239696 18.571364015563038 19.700650420240237 0.7393206976024979 4.309450546828799 4.438541474430563 0.8598375995515071
user_002 Jogging 1.446034908139e12 -16.20889 -13.83303 -8.43107 -5.102970909090908 -0.7588395454545455 -2.811918363636364 262.7281150321 191.35271898090002 71.08294134490001 22.91645206741 7.7895724282934165 11.105919090909092 13.074190454545455 5.619151636363636 3.8196790082644627 5.613133347107438 1.4023345041322315 123.34143885381903 170.9344560417275 31.57486511244813 22.279454978312547 45.07532239502894 3.9238172475664856 4.720111754854174 6.713815785008473 1.9808627533391823
user_002 Jogging 1.446034908269e12 -3.67815 -1.76214 1.49389 -5.963435454545455 -1.3824163636363638 -2.7317938181818175 13.5287874225 3.1051373796000004 2.2317073320999996 4.343458545237885 8.741728257991952 2.285285454545455 0.37972363636363626 4.2256838181818175 3.8149286776859497 5.324939834710744 1.9438858264462808 5.222529608757027 0.14419004001322305 17.856403731243663 23.576699133056877 43.9105411464654 6.288745057720135 4.855584324574837 6.626502934917134 2.5077370391889446
user_002 Jogging 1.446034909046e12 -5.05768 -1.07237 -0.652044 -9.196275454545455 -6.566109090909092 -2.5088374545454544 25.580126982400003 1.1499774169 0.42516137793599995 5.211071461536101 12.418203811353674 4.138595454545455 5.4937390909090915 1.8567934545454543 4.934770495867768 5.036428710743802 2.7267596363636364 17.127972336384303 30.18116919898265 3.447681932842842 33.161018213630584 33.540879014491985 12.511976010260918 5.758560428929315 5.791448783723464 3.5372271640737067
user_002 Jogging 1.446034910211e12 -17.05194 -11.6871 -1.07357 -8.475157272727273 -6.458115909090908 -2.310269909090909 290.76865776359995 136.58830640999997 1.1525525448999998 20.700471412953377 11.878641916477324 8.576782727272725 5.228984090909091 1.2366999090909092 6.322850239669421 4.93666985123967 2.176657570247934 73.56120195084377 27.342274622980376 1.529426665145463 49.513870967071085 29.244915742785835 8.943415354326099 7.036609337391915 5.407856853022816 2.9905543556882725
user_002 Jogging 1.446034910923e12 -15.0976 -14.3312 1.49389 -7.0747254545454545 -5.541911818181819 -2.4983859090909095 227.93752576 205.38329344000002 2.2317073320999996 20.869895220918096 10.728633853208215 8.022874545454545 8.789288181818183 3.9922759090909095 5.452567685950413 4.862880545454545 2.2213097768595045 64.36651597210248 77.25158674304878 15.938266934307647 42.44141270557199 30.712884458420195 8.367651130529412 6.514707415193103 5.541920647069948 2.892689255784211
user_002 Jogging 1.446034911246e12 -4.75112 -6.39889 0.880768 -6.914476363636364 -5.099486363636363 -1.561280909090909 22.573141254400003 40.945793232099994 0.775752269824 8.01839676969929 10.070073140367551 2.163356363636364 1.2994036363636363 2.442048909090909 5.080449173553718 4.724800603305787 1.8662933884297523 4.680110756085952 1.6884498101950411 5.963602874392099 38.99996173856371 29.48726106588099 4.7361626274450375 6.24499493503107 5.430217405029102 2.1762726454755246
user_002 Jogging 1.446034912153e12 -17.93331 -10.53749 -8.23947 -8.192980727272726 -5.761382454545454 -2.0733795454545456 321.6036075561 111.0386955001 67.88886588090001 22.372553920755227 11.34494337446847 9.740329272727273 4.776107545454546 6.166090454545455 6.011221520661156 4.700413702479339 1.9571871735537187 94.8740143411478 22.811203285747848 38.02067149363658 47.0317002322874 26.73019534190938 7.5335368870795465 6.857966187747458 5.170125273328431 2.744728927795885
user_002 Jogging 1.44603491306e12 -0.957409 1.91661 1.22565 -9.095248999999999 -6.325737 -2.470517545454545 0.9166319932809999 3.6733938920999996 1.5022179224999999 2.468247112402038 12.124781946634904 8.137839999999999 8.242347 3.696167545454545 4.828992140495868 4.8625619173553725 2.2665985950413226 66.22443986559998 67.93628406840901 13.661654524071476 33.47302909714301 31.912813317328006 7.9159821938666335 5.785588051109672 5.649142706404929 2.8135355327179776
user_002 Jogging 1.446034913319e12 -17.85667 -13.41151 -1.80165 -8.078019 -5.792736090909091 -2.1569866363636367 318.86066348890006 179.86860048009999 3.2459427224999997 22.404803205819505 11.181984622796081 9.778651000000002 7.618773909090909 0.35533663636363677 5.500073561983472 5.078866123966942 2.0981160330578517 95.62201537980104 58.04571587784437 0.12626412514222343 41.78944792661123 32.60139135892502 6.684421911083967 6.464475843145462 5.7097628110916325 2.5854248995250213
user_002 Jogging 1.446034914095e12 -17.39682 -10.49917 -3.56439 -8.861844909090909 -5.841506090909092 -1.6866936363636365 302.64934611240005 110.23257068889998 12.7048760721 20.629755036679423 11.92481561399505 8.534975090909093 4.657663909090908 1.8776963636363635 5.914944851239668 4.972139173553718 2.1484710495867767 72.84579980243868 21.693833090047995 3.5257436340132227 46.87801609592091 27.69571628107252 7.233094173347625 6.846752229774414 5.262671971638791 2.6894412381287727
user_002 Jogging 1.446034914937e12 -14.06296 -9.31124 0.344284 -10.049774545454547 -6.2351611818181825 -0.21658654545454545 197.76684396160002 86.6991903376 0.11853147265599999 16.86963442911126 12.252088776393206 4.013185454545454 3.0760788181818173 0.5608705454545454 5.10451879338843 4.026167958677686 2.1858417190082644 16.1056574925752 9.462260895666846 0.31457576875847926 34.7920575256337 20.439095374185214 5.985408657440974 5.898479255336388 4.520961775351038 2.446509484437159
user_002 Jogging 1.446034915132e12 -3.79311 -0.650847 0.267643 -8.910616363636363 -4.698865454545454 -0.1364618181818182 14.387683472099999 0.42360181740899994 7.163277544900001e-2 3.8578385224057783 10.584969232379587 5.1175063636363625 4.0480184545454545 0.4041048181818182 4.847044462809918 4.361232578512396 1.7323318264462806 26.188871381858664 16.38645340834057 0.16330070407776034 29.31876509625081 22.243799336105926 4.342268189926172 5.4146805165448875 4.716333251171499 2.083810977494401
user_002 Jogging 1.446034915455e12 1.76333 -1.72382 -0.345482 -10.067193636363639 -5.4374033636363635 -1.052664909090909 3.1093326889000004 2.9715553923999996 0.119357812324 2.4900292957360963 12.23813765690058 11.830523636363639 3.7135833636363635 0.707182909090909 5.288836694214875 4.095206685950413 1.8130885867768596 139.96128951055874 13.790701398676768 0.5001076669102809 38.75524016966116 20.051422205409718 7.297770799175755 6.22537068532157 4.4778814416428805 2.701438653602142
user_002 Jumping 1.446035033798e12 -1.30229 0.307161 -0.920286 -6.6575549999999994 -7.12697975 0.7179085000000001 1.6959592440999998 9.434787992100001e-2 0.8469263217960001 1.6239561095722383 10.874421038711667 5.355264999999999 7.43414075 1.6381945 3.794508333333333 5.764013104166667 1.3292357083333333 28.678863220224994 55.26644869081056 2.68368121983025 20.47484638194861 50.37997567727834 2.93820038376659 4.524913964038278 7.0978852961483065 1.7141179608669266
user_002 Jumping 1.446035033863e12 -0.344284 -0.535886 0.344284 -5.394900799999999 -5.8087610000000005 0.6431836000000001 0.11853147265599999 0.287173804996 0.11853147265599999 0.7240419534170655 8.844345221652747 5.050616799999999 5.272875000000001 0.2988996000000001 4.045730026666666 5.665785483333333 1.1231684866666667 25.508730060442232 27.80321076562501 8.934097088016006e-2 21.481623117647334 45.86462269494767 2.368428501189304 4.634827193935857 6.7723424821067395 1.5389699481111723
user_002 Jumping 1.446035033927e12 -0.842448 -0.650847 -1.26517 -4.636158666666666 -4.949108666666667 0.32512466666666673 0.7097186327039999 0.42360181740899994 1.6006551288999997 1.6534737914502906 7.645866649952336 3.793710666666666 4.298261666666667 1.5902946666666666 4.0037268 5.437864847222222 1.20102285 14.392240622380438 18.47505335513611 2.5290371268284444 20.300059368436184 41.29969447164574 2.3951966054624942 4.505558718786848 6.42648383423204 1.5476422730923622
user_002 Jumping 1.446035034057e12 -6.70546 -11.6871 0.842448 -4.46850775 -5.37382525 0.20537325000000006 44.96319381160001 136.58830640999997 0.7097186327039999 13.50041550672808 7.712791209417686 2.2369522500000008 6.313274749999999 0.6370747499999999 3.647825774107143 5.225442836309524 1.1384730526785716 5.0039553687800655 39.85743806898755 0.40586423708756236 16.918744297309093 36.98160318013506 2.0470234572839994 4.11324012152331 6.081250133001854 1.4307422749342382
user_002 Jumping 1.446035034445e12 -1.76214 -0.267643 -0.996927 -4.765055181818181 -5.541912 0.2571926363636364 3.1051373796000004 7.163277544900001e-2 0.993863443329 2.042212917004003 7.982462080994015 3.002915181818181 5.274269 1.2541196363636364 4.781736989249638 6.35182557994228 1.1887342204971796 9.01749958919412 27.817913484361004 1.5728160623128598 31.74650931534741 50.318931638349575 2.334578496357329 5.634404078103327 7.093583835999231 1.5279327525638453
user_002 Jumping 1.446035035417e12 -7.1653 -11.61046 0.995729 -6.830867636363636 -8.680694454545455 0.25719163636363634 51.34152409 134.8027814116 0.991476241441 13.679758102504628 11.519586108272428 0.3344323636363642 2.9297655454545453 0.7385373636363637 4.467641735537191 6.43369567768595 0.7800238347107438 0.11184500584740534 8.583526151332569 0.5454374374869505 27.654650666007146 49.408091581727376 0.6421275864403456 5.258768930653556 7.029088958160038 0.801328638225507
user_002 Jumping 1.446035036064e12 0.652044 0.881966 -1.11189 -5.5419113636363635 -6.719390818181818 -0.2897428181818182 0.42516137793599995 0.7778640251560001 1.2362993721000002 1.561833786032304 9.428134272108517 6.193955363636364 7.601356818181818 0.8221471818181818 4.442940404958677 6.1952234876033065 0.7898413223140497 38.365083046719676 57.78062547731922 0.6759259885715785 26.80721992624767 44.61862266479724 0.8233101719703998 5.177568920472973 6.6797172593454315 0.907364409689073
user_002 Jumping 1.446035036647e12 -0.459245 -2.14534 -0.767005 -5.242317090909091 -6.984149545454546 4.4688181818181814e-2 0.210905970025 4.6024837156 0.5882966700250001 2.3241528253645454 9.347194647011769 4.783072090909091 4.838809545454546 0.8116931818181818 4.471758231404959 6.197756520661158 0.8256284876033056 22.87777862683346 23.41407781718203 0.658845821410124 24.532754052048745 43.48848930565539 0.8307662014794853 4.9530550221099645 6.594580297915508 0.9114637686049212
user_002 Jumping 1.446035041373e12 -0.535886 -1.64717 -1.03525 -5.538427636363636 -7.430056727272727 -0.43257309090909096 0.287173804996 2.7131690089 1.0717425625 2.0179408753469463 9.764384790075978 5.002541636363636 5.782886727272727 0.602676909090909 4.196865702479339 5.813602826446282 0.5177994214876033 25.025422823551768 33.44177890046707 0.3632194567513718 22.45182419827358 38.34933714049541 0.40652773556788735 4.73833559367354 6.1926841628243405 0.6375952756787705
user_002 Jumping 1.44603504215e12 -1.14901 -0.420925 0.344284 -4.291276363636364 -6.2247104545454555 -0.509214 1.3202239801000002 0.177177855625 0.11853147265599999 1.2711936549483718 8.034460275069408 3.1422663636363644 5.803785454545455 0.8534980000000001 3.6496149421487605 6.059993644628099 0.4718784380165289 9.8738379000405 33.683925602393394 0.7284588360040002 18.037898103949008 41.549573370724985 0.2748523318328828 4.247104673062463 6.445895854784266 0.5242636091060325
user_002 Jumping 1.446035042538e12 -3.63983 -3.86975 -0.383802 -5.1761277272727275 -8.179046636363637 -0.6102402727272728 13.248362428899998 14.974965062499999 0.147303975204 5.326408871519722 10.024669937451387 1.5362977272727276 4.309296636363637 0.2264382727272728 3.2996652644628095 5.7654663553719 0.49024671900826444 2.360210706823348 18.57003750017496 5.127429135571077e-2 14.209285799045562 38.99125749161312 0.2935062012731563 3.769520632526842 6.244297998303182 0.5417621260970135
user_002 Jumping 1.446035042926e12 -10.11596 -15.25089 3.7722e-2 -5.256252272727273 -8.29400809090909 -0.7739722727272725 102.33264672159999 232.58964579210001 1.422949284e-3 18.30092116432897 10.515775377709382 4.859707727272727 6.95688190909091 0.8116942727272726 3.8808028760330573 6.340904438016529 0.6865985123966943 23.616759194514252 48.39820589703639 0.658847592378256 18.500328994784294 45.368967180312275 0.8470754660074215 4.301200878218117 6.735648979891416 0.9203670278793246
user_002 Jumping 1.446035043445e12 -3.56319 -7.81675 -1.34181 -4.611774090909091 -6.754229181818181 -1.1641431818181818 12.696322976100001 61.1015805625 1.8004540760999999 8.694731601073146 8.943475057995606 1.0485840909090913 1.0625208181818184 0.17766681818181818 3.6682985206611574 5.689458504132232 0.9301391074380163 1.0995285957076455 1.1289504890697608 3.156549828285124e-2 18.615440480806782 42.168303896146696 1.3272466957004447 4.314561447100595 6.493712643484211 1.1520619322330048
user_002 Jumping 1.446035043574e12 -14.36952 -19.58108 0.420925 -6.416312272727273 -9.380912181818182 -0.700815909090909 206.4831050304 383.4186939664 0.177177855625 24.29154126136143 12.046808337182016 7.953207727272726 10.200167818181818 1.121740909090909 4.3900503388429755 6.595844338842975 1.0026629669421487 63.25351315315061 104.04342351907202 1.2583026671280988 25.11940654493285 53.231245821914314 1.426878065493329 5.011926430518793 7.29597463139191 1.1945200146893016
user_002 Jumping 1.446035043638e12 -13.64143 -17.24354 -0.1922 -6.736809545454546 -9.562062181818181 -0.721717909090909 186.08861244489998 297.3396717316 3.694084e-2 21.987842663992755 12.381983018969633 6.904620454545454 7.681477818181818 0.529517909090909 4.575951495867769 6.661716694214875 0.9770105702479338 47.67378362132747 59.00510147121931 0.2803892160480082 27.306408765552234 54.19550905593094 1.3924727585542156 5.225553441077054 7.3617599156676485 1.1800308294931179
user_002 Jumping 1.446035044156e12 -15.21256 -18.89131 -0.767005 -6.479016363636364 -8.948935545454544 -0.46740981818181826 231.4219817536 356.88159351610005 0.5882966700250001 24.267094427222332 11.74871380185931 8.733543636363635 9.942374454545456 0.2995951818181818 4.947753066115702 6.188887628099172 0.6663303057851239 76.27478444826774 98.85080979439806 8.975727296866941e-2 29.89711555340259 46.60736227828711 0.736107912280498 5.467825486736257 6.826958493962528 0.8579673142261878
user_002 Jumping 1.446035044545e12 -0.650847 -0.420925 0.267643 -5.46527009090909 -6.9109917272727275 -0.8715146363636365 0.42360181740899994 0.177177855625 7.163277544900001e-2 0.8200075905032831 9.38892652315506 4.814423090909091 6.490066727272728 1.1391576363636364 4.232968380165289 6.326651388429752 0.7106671983471075 23.178669698278643 42.120966124452536 1.297680120485587 23.35106811043113 46.895908393370604 0.6108041687504081 4.8322942905447235 6.848058731740741 0.7815396143193306
user_002 Jumping 1.446035045839e12 -8.85139 -11.72542 0.305964 -5.521009272727273 -7.200136545454544 -0.35593254545454545 78.34710493210001 137.4854741764 9.361396929600001e-2 14.694427279679736 9.497917300387376 3.3303807272727273 4.525283454545455 0.6618965454545455 4.381500247933884 5.622635090909091 0.6425778429752066 11.091435788589619 20.478190343982853 0.4381070368846612 23.812058545512084 36.44259565766158 0.590843696719027 4.879760090979072 6.036770300223587 0.7686635783741982
user_002 Jumping 1.446035046098e12 -3.29495 -4.59784 -0.15388 -5.844989272727273 -8.078020181818182 -0.742618909090909 10.856695502500001 21.140132665599996 2.3679054399999996e-2 5.658666558695608 10.38518386833713 2.5500392727272727 3.4801801818181826 0.588738909090909 4.263687842975207 5.87725885123967 0.7185846528925619 6.502700292451438 12.111654097920038 0.34661350307755356 20.709634302860838 39.065419343592374 0.8314188977151395 4.550783921794226 6.250233543123999 0.911821746678121
user_002 Jumping 1.44603504681e12 -0.229323 0.1922 -0.498763 -4.876532181818181 -6.099299000000001 -0.7286840000000001 5.2589038329e-2 3.694084e-2 0.24876453016900002 0.5816308180435421 8.625721908563833 4.647209181818181 6.291499000000001 0.2299210000000001 4.378649504132231 6.121748975206612 0.6143912975206612 21.59655317957521 39.58295966700101 5.286366624100004e-2 23.7805886174197 45.32605095967318 0.49155458285741943 4.876534488488695 6.732462473692162 0.7011095369893491
user_002 Jumping 1.446035046875e12 -0.842448 -1.03405 -0.345482 -4.9636238181818175 -6.322253545454546 -0.6276578181818181 0.7097186327039999 1.0692594024999997 0.119357812324 1.377801091423577 8.565835701140356 4.121175818181817 5.288203545454547 0.2821758181818181 4.2956750578512395 5.860474157024794 0.5868385950413223 16.984090124366574 27.96509673815804 7.962319236657846e-2 23.020951708247193 41.81179228320366 0.4676545045738995 4.798015392664679 6.466203854132938 0.6838526921595758
user_002 Jumping 1.446035047198e12 -13.21991 -16.63042 0.420925 -7.189685909090908 -9.31123781818182 -0.6172074545454546 174.76602040810002 276.5708693764 0.177177855625 21.248860384503566 12.192681806384348 6.030224090909092 7.3191821818181815 1.0381324545454547 5.007293181818182 6.497985338842975 0.5244497603305786 36.36360258658039 53.57042781064475 1.0777189931805704 30.092576058743646 51.20800629042747 0.39204926912054333 5.485670064699812 7.1559769626814385 0.6261383785718164
user_002 Jumping 1.446035047263e12 -4.06135 -5.90073 -3.8919e-2 -6.175939545454545 -8.067569636363636 -0.5301158181818182 16.4945638225 34.8186145329 1.514688561e-3 7.163427464835601 10.58790123368122 2.114589545454545 2.166839636363636 0.4911968181818182 4.47302656198347 5.761348685950413 0.5618199338842975 4.4714889457456595 4.695194009716494 0.24127431419194217 24.693217809402338 42.04669015402345 0.4133996612237356 4.969227083702489 6.48434192143069 0.6429616327773654
user_002 Jumping 1.446035048687e12 -0.650847 -1.95374 7.6042e-2 -4.9009182727272735 -6.210774181818182 -0.8749986363636364 0.42360181740899994 3.8170999876000002 5.782385764e-3 2.0606999273967572 8.582328109355055 4.250071272727274 4.257034181818182 0.9510406363636363 4.732400454545455 5.830070454545455 0.7724236694214877 18.06310582326163 18.1223400251684 0.9044782920149503 26.822176913056808 41.98446965925354 0.8800927343924942 5.179013121537423 6.479542395821911 0.938132578259861
user_002 Jumping 1.446035049399e12 -13.52647 -17.3585 -0.958607 -6.747261090909091 -8.673726545454544 -0.18174954545454547 182.9653906609 301.31752224999997 0.918927380449 22.027297616624445 11.464334396480872 6.779208909090909 8.684773454545455 0.7768574545454545 4.79384026446281 5.962767528925619 0.6299100495867768 45.957673433097554 75.4252899567774 0.603507504682843 28.706956726588132 41.384309342338895 0.6132338470071389 5.357887337989492 6.433063760164273 0.7830924894334889
user_002 Jumping 1.4460350505e12 -6.24561 -9.73276 -1.15021 -5.1587095454545455 -7.287228 -0.35593318181818184 39.0076442721 94.72661721760001 1.3229830441 11.62141319004707 9.455231050646873 1.0869004545454546 2.445532000000001 0.7942768181818181 3.9922799008264462 5.749314008264463 0.5428184214876032 1.1813525980911157 5.980626763024005 0.6308756639010329 21.690321855347296 39.86753617989176 0.427005639025329 4.657286962958938 6.314074451563884 0.6534566848883934
user_002 Sitting 1.44603456478e12 -0.765807 -0.114362 9.4262 -0.765807 -0.114362 9.4262 0.586460361249 1.3078667044000002e-2 88.85324643999999 9.457948269487044 9.457948269487044 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
user_002 Sitting 1.446034565169e12 -0.842448 -0.152682 9.4262 -0.8205507142857142 -0.1417335714285714 9.431674285714285 0.7097186327039999 2.3311793124000002e-2 88.85324643999999 9.465002739874299 9.468437272237447 2.189728571428573e-2 1.0948428571428609e-2 5.474285714285543e-3 1.6631628911564604e-2 1.86257112244898e-2 1.611004081632699e-2 4.7949112165306194e-4 1.198680881836743e-4 2.9967804081630776e-5 5.057707334111117e-4 4.989748108321516e-4 4.2989052794818944e-4 2.2489347109489678e-2 2.233774408556405e-2 2.073380157974387e-2
user_002 Sitting 1.446034565688e12 -0.919089 -3.7722e-2 9.4262 -0.8389643636363636 -0.13874772727272727 9.433167272727273 0.8447245899210001 1.422949284e-3 88.85324643999999 9.470976400519906 9.471666852469868 8.012463636363643e-2 0.10102572727272727 6.967272727273155e-3 3.203548127705629e-2 4.438884426406926e-2 1.5275845992391623e-2 6.4199573524049685e-3 1.020619757098347e-2 4.854288925620431e-5 1.4169701993062044e-3 2.985819414044147e-3 4.3332102977010464e-4 3.764266461485165e-2 5.464265196752576e-2 2.0816364470533866e-2
user_002 Sitting 1.446034566658e12 -0.727487 -0.305964 9.54116 -0.7692910909090908 -0.16313345454545455 9.447101818181817 0.529237335169 9.361396929600001e-2 91.0337341456 9.57374458872102 9.480753256798605 4.180409090909076e-2 0.14283054545454546 9.405818181818226e-2 8.455804958677687e-2 5.732220661157026e-2 4.180363636363635e-2 1.747582016735525e-3 2.0400564714842976e-2 8.846941566942232e-3 1.325132104521563e-2 4.601724310780617e-3 2.299167754770868e-3 0.1151143824429234 6.783601042794761e-2 4.794963769175809e-2
user_002 Sitting 1.446034567047e12 -0.765807 -0.152682 9.46452 -0.7832257272727273 -0.18055172727272728 9.436650909090906 0.586460361249 2.3311793124000002e-2 89.5771388304 9.496678945019307 9.471570465860033 1.7418727272727308e-2 2.7869727272727268e-2 2.7869090909094396e-2 5.763904132231403e-2 6.555633884297521e-2 3.705322314049604e-2 3.034120598016541e-4 7.76721698256198e-4 7.766862280993679e-4 7.076373251673926e-3 6.461827551674681e-3 1.9317863429000853e-3 8.412118194410921e-2 8.03854934156324e-2 4.3952091450806814e-2
user_002 Sitting 1.446034567111e12 -0.765807 -0.114362 9.4262 -0.75884 -0.1666170909090909 9.436650909090908 0.586460361249 1.3078667044000002e-2 88.85324643999999 9.457948269487044 9.468972667311892 6.9670000000000565e-3 5.2255090909090904e-2 1.0450909090907956e-2 3.578690082644627e-2 6.143933057851239e-2 3.546975206611594e-2 4.853908900000079e-5 2.7305945259173546e-3 1.0922150082642256e-4 1.519209039241922e-3 5.845110941862509e-3 1.8711077313298444e-3 3.897703220156612e-2 7.645332525052465e-2 4.325630279311726e-2
user_002 Sitting 1.446034567241e12 -0.804128 -0.114362 9.46452 -0.7727747272727273 -0.17358445454545457 9.440134545454544 0.646621840384 1.3078667044000002e-2 89.5771388304 9.499307308316117 9.473686950322545 3.135327272727262e-2 5.9222454545454564e-2 2.4385454545456042e-2 3.3253355371900814e-2 6.0172553719008266e-2 3.515305785123989e-2 9.83027710710737e-4 3.507299122388432e-3 5.946503933885027e-4 1.3095898869752052e-3 5.8164262194012025e-3 1.7949836549962473e-3 3.618825620246443e-2 7.626549822430326e-2 4.23672474323769e-2
user_002 Sitting 1.446034568082e12 -0.689167 -0.191003 9.4262 -0.7553561818181819 -0.156166 9.429683636363636 0.47495115388899994 3.6482146009e-2 88.85324643999999 9.45328936084673 9.461340420717299 6.61891818181819e-2 3.483700000000001e-2 3.4836363636365775e-3 2.0585446280991692e-2 3.64201570247934e-2 2.406876033057886e-2 4.381007789760341e-3 1.2136165690000004e-3 1.2135722314051077e-5 7.68973975536438e-4 1.973744353509392e-3 7.92131692862547e-4 2.77303800106749e-2 4.442684271371748e-2 2.8144834212738702e-2
user_002 Sitting 1.446034569054e12 -0.765807 -0.191003 9.38788 -0.7553561818181819 -0.14223136363636366 9.433167272727273 0.586460361249 3.6482146009e-2 88.13229089439999 9.420999596733777 9.464589357092626 1.0450818181818144e-2 4.877163636363635e-2 4.528727272727373e-2 2.7235760330578507e-2 3.4520107438016534e-2 4.1803636363636994e-2 1.0921960066942071e-4 2.3786725135867756e-3 2.050937071074471e-3 1.3459775338459804e-3 2.280452508866266e-3 2.2395923906837365e-3 3.6687566474842406e-2 4.775408368785088e-2 4.732433190953399e-2
user_002 Sitting 1.446034569312e12 -0.727487 -0.152682 9.4262 -0.7379379090909091 -0.1352639090909091 9.429683636363634 0.529237335169 2.3311793124000002e-2 88.85324643999999 9.455463794457307 9.459572879689434 1.0450909090909066e-2 1.741809090909091e-2 3.483636363634801e-3 2.153520661157021e-2 2.7869371900826445e-2 2.4702148760331447e-2 1.0922150082644576e-4 3.0338989091735545e-4 1.21357223140387e-5 6.707759668279468e-4 1.524711514772352e-3 1.0194006743802228e-3 2.589934298062302e-2 3.904755452998756e-2 3.192805466012959e-2
user_002 Sitting 1.446034569443e12 -0.727487 -0.152682 9.4262 -0.7449052727272728 -0.14571481818181817 9.429683636363636 0.529237335169 2.3311793124000002e-2 88.85324643999999 9.455463794457307 9.460267960270265 1.741827272727281e-2 6.9671818181818446e-3 3.4836363636365775e-3 2.3752140495867744e-2 1.741833884297521e-2 1.8051570247934832e-2 3.033962248016558e-4 4.8541622487603674e-5 1.2135722314051077e-5 8.925379239271204e-4 6.343758824335087e-4 5.858244135237135e-4 2.9875373201470143e-2 2.5186819617282145e-2 2.4203809896867757e-2
user_002 Sitting 1.446034569896e12 -0.765807 -0.152682 9.4262 -0.7518726363636362 -0.14919836363636363 9.436650909090908 0.586460361249 2.3311793124000002e-2 88.85324643999999 9.458489234247349 9.467781289695454 1.39343636363638e-2 3.483636363636383e-3 1.0450909090907956e-2 2.4068917355371876e-2 1.2034322314049604e-2 1.74181818181824e-2 1.9416648995041779e-4 1.2135722314049723e-5 1.0922150082642256e-4 8.362799605987959e-4 1.8313804574830977e-4 4.909451299774928e-4 2.8918505504240636e-2 1.353285061427598e-2 2.2157281646842258e-2
user_002 Sitting 1.446034570996e12 -0.765807 -0.114362 9.4262 -0.7623234545454545 -0.15964954545454543 9.429683636363636 0.586460361249 1.3078667044000002e-2 88.85324643999999 9.457948269487044 9.461895649839656 3.4835454545455447e-3 4.528754545454543e-2 3.4836363636365775e-3 1.266781818181819e-2 3.166985123966942e-2 2.6919008264463008e-2 1.2135088933884925e-5 2.050961773297518e-3 1.2135722314051077e-5 3.552524841622832e-4 1.5004470374380165e-3 1.1639260946656388e-3 1.884814272447774e-2 3.873560426065426e-2 3.411636109941444e-2
user_002 Sitting 1.446034571061e12 -0.765807 -0.152682 9.46452 -0.7623234545454545 -0.15268218181818183 9.433167272727273 0.586460361249 2.3311793124000002e-2 89.5771388304 9.496678945019307 9.465226755939694 3.4835454545455447e-3 1.8181818181584042e-7 3.135272727272742e-2 1.266782644628101e-2 2.5335917355371895e-2 2.691900826446317e-2 1.2135088933884925e-5 3.3057851238818004e-14 9.829935074380258e-4 3.5525254174079574e-4 1.0591388312321563e-3 1.1639260946656493e-3 1.8848144251909674e-2 3.25444132107518e-2 3.411636109941459e-2
user_002 Sitting 1.446034571579e12 -0.727487 -0.229323 9.4262 -0.7623234545454545 -0.1666169090909091 9.440134545454544 0.529237335169 5.2589038329e-2 88.85324643999999 9.45701183321127 9.472428728452309 3.4836454545454476e-2 6.27060909090909e-2 1.3934545454544534e-2 1.1401074380165273e-2 2.7236082644628092e-2 2.8185785123967057e-2 1.213578565297516e-3 3.932053837099173e-3 1.941715570247677e-4 3.5966524376709197e-4 1.3084813420150261e-3 1.1551001148009435e-3 1.8964842307994337e-2 3.617293659650853e-2 3.398676381771209e-2
user_002 Sitting 1.44603457242e12 -0.727487 -0.152682 9.46452 -0.7449052727272726 -0.15964963636363638 9.429683636363633 0.529237335169 2.3311793124000002e-2 89.5771388304 9.493665675527708 9.460525402885743 1.7418272727272588e-2 6.96763636363637e-3 3.483636363636755e-2 3.0719429752066107e-2 2.4069231404958678e-2 2.8819173553719324e-2 3.0339622480164805e-4 4.854795649586786e-5 1.2135722314052313e-3 1.4662266727175069e-3 7.303726936025546e-4 1.2874898127723882e-3 3.829133939571071e-2 2.7025408296685448e-2 3.588160828018148e-2
user_002 Sitting 1.446034572485e12 -0.727487 -7.6042e-2 9.46452 -0.7449052727272728 -0.14919863636363637 9.436650909090908 0.529237335169 5.782385764e-3 89.5771388304 9.492742414673064 9.46732361206275 1.741827272727281e-2 7.315663636363637e-2 2.786909090909262e-2 2.976934710743803e-2 2.9136322314049588e-2 2.6285619834711227e-2 3.033962248016558e-4 5.351893444041323e-3 7.766862280992689e-4 1.4231998481344878e-3 1.1893258346273481e-3 1.075666296018078e-3 3.772532104746741e-2 3.448660369806438e-2 3.279735196655483e-2
user_002 Sitting 1.446034573133e12 -0.765807 -0.152682 9.4262 -0.7518726363636364 -0.1491987272727273 9.436650909090908 0.586460361249 2.3311793124000002e-2 88.85324643999999 9.458489234247349 9.467899249887088 1.3934363636363578e-2 3.4832727272727237e-3 1.0450909090907956e-2 2.6919157024793385e-2 3.705350413223141e-2 1.551801652892512e-2 1.941664899504116e-4 1.2133188892561959e-5 1.0922150082642256e-4 1.007281305137491e-3 1.8832758142344102e-3 2.7470862329075655e-4 3.173769533437315e-2 4.339672584693931e-2 1.6574336285075084e-2
user_002 Sitting 1.446034573262e12 -0.765807 -0.114362 9.46452 -0.7518725454545454 -0.1491987272727273 9.440134545454544 0.586460361249 1.3078667044000002e-2 89.5771388304 9.496140155805042 9.471356114557238 1.3934454545454611e-2 3.483672727272728e-2 2.4385454545456042e-2 2.3435413223140508e-2 3.7686917355371906e-2 1.678479338842949e-2 1.9416902347934065e-4 1.2135975670743808e-3 5.946503933885027e-4 8.208248797753583e-4 1.9229953147746053e-3 3.1883852261458203e-4 2.8650041531826063e-2 4.385197047767187e-2 1.785605002834003e-2
user_002 Sitting 1.446034573392e12 -0.765807 -0.152682 9.38788 -0.7518725454545454 -0.145715 9.433167272727273 0.586460361249 2.3311793124000002e-2 88.13229089439999 9.420300581657306 9.46434959120047 1.3934454545454611e-2 6.967000000000001e-3 4.528727272727373e-2 2.3435413223140508e-2 3.483659504132232e-2 1.931834710743775e-2 1.9416902347934065e-4 4.8539089000000014e-5 2.050937071074471e-3 8.119984968407226e-4 1.7674321221953415e-3 4.732931702479435e-4 2.849558732226312e-2 4.204083874276703e-2 2.1755302118057186e-2
user_002 Sitting 1.446034573455e12 -0.689167 -0.152682 9.38788 -0.7518725454545454 -0.14223127272727273 9.4262 0.47495115388899994 2.3311793124000002e-2 88.13229089439999 9.414380162358698 9.457338697442692 6.270554545454543e-2 1.0450727272727278e-2 3.8320000000000576e-2 2.3435404958677686e-2 3.1669578512396705e-2 2.0585123966941798e-2 3.931985430752063e-3 1.0921770052892573e-4 1.4684224000000442e-3 8.119974603846732e-4 1.590906939531931e-3 5.52726989030811e-4 2.849556913600206e-2 3.988617479192422e-2 2.351014651232125e-2
user_002 Sitting 1.446034573521e12 -0.727487 -0.114362 9.46452 -0.7483889090909092 -0.13178027272727272 9.429683636363636 0.529237335169 1.3078667044000002e-2 89.5771388304 9.493126715293176 9.460346873567627 2.0901909090909165e-2 1.7418272727272713e-2 3.4836363636364e-2 2.4068818181818195e-2 2.628573553719008e-2 2.2485289256198113e-2 4.368898036446312e-4 3.033962248016524e-4 1.213572231404984e-3 8.340632161750568e-4 1.0845090320075132e-3 6.453997776108307e-4 2.8880152634206364e-2 3.293188473208773e-2 2.540471959323367e-2
user_002 Sitting 1.44603457378e12 -0.804128 -0.114362 9.4262 -0.748388909090909 -0.13874763636363638 9.426199999999996 0.646621840384 1.3078667044000002e-2 88.85324643999999 9.461128206901542 9.4570153963809 5.5739090909090905e-2 2.4385636363636373e-2 3.552713678800501e-15 2.5018917355371924e-2 3.325310743801653e-2 2.121851239669487e-2 3.1068462553719e-3 5.946592608595046e-4 1.2621774483536189e-29 9.057764906649138e-4 1.7641233586235911e-3 7.160076165289551e-4 3.0096120857428018e-2 4.20014685293692e-2 2.6758318641666466e-2
user_002 Sitting 1.446034574557e12 -0.727487 -0.191003 9.38788 -0.7449053636363636 -0.16661700000000002 9.436650909090908 0.529237335169 3.6482146009e-2 88.13229089439999 9.417962113725983 9.467609675926727 1.741836363636362e-2 2.438599999999999e-2 4.877090909090853e-2 3.198629752066117e-2 2.6919380165289254e-2 2.8185785123967865e-2 3.033993917685945e-4 5.946769959999995e-4 2.3786015735536644e-3 1.3537044120946666e-3 1.1264441829564242e-3 1.1948170241924013e-3 3.679272227077886e-2 3.356254136617822e-2 3.456612538588034e-2
user_002 Sitting 1.446034574622e12 -0.765807 -0.114362 9.46452 -0.7483889999999999 -0.16661700000000002 9.44361818181818 0.586460361249 1.3078667044000002e-2 89.5771388304 9.496140155805042 9.474829731901304 1.7418000000000156e-2 5.225500000000001e-2 2.0901818181819465e-2 3.1986272727272766e-2 2.913626446280992e-2 2.7552396694216084e-2 3.033867240000054e-4 2.730585025000001e-3 4.368860033058388e-4 1.3537035483854264e-3 1.304070425015778e-3 1.1639260946657436e-3 3.679271053327583e-2 3.611191527758917e-2 3.411636109941597e-2
user_002 Sitting 1.446034576823e12 -0.727487 -0.191003 9.4262 -0.7518726363636364 -0.1666169090909091 9.422716363636361 0.529237335169 3.6482146009e-2 88.85324643999999 9.456160210211014 9.454272305984539 2.4385636363636443e-2 2.4386090909090913e-2 3.483636363638354e-3 2.7869264462809906e-2 2.7869404958677693e-2 2.7552396694216084e-2 5.94659260859508e-4 5.946814298264465e-4 1.2135722314063454e-5 1.0657548036927113e-3 1.4430797806025554e-3 1.042568871525224e-3 3.2645900258573224e-2 3.7987889920375356e-2 3.228883509086731e-2
user_002 Sitting 1.446034577018e12 -0.727487 -0.114362 9.4262 -0.7553562727272727 -0.16661700000000002 9.408781818181815 0.529237335169 1.3078667044000002e-2 88.85324643999999 9.454922656596032 9.440658106002388 2.7869272727272687e-2 5.225500000000001e-2 1.7418181818184664e-2 2.4385636363636352e-2 3.51535041322314e-2 2.4385454545455074e-2 7.766963623471052e-4 2.730585025000001e-3 3.033930578513388e-4 7.822206036093154e-4 1.9318294136048094e-3 8.10886900075132e-4 2.7968207014560577e-2 4.395258142140015e-2 2.847607592480277e-2
user_002 Sitting 1.446034577212e12 -0.765807 -0.191003 9.38788 -0.75884 -0.16661700000000002 9.408781818181815 0.586460361249 3.6482146009e-2 88.13229089439999 9.420999596733777 9.440918817313054 6.9670000000000565e-3 2.438599999999999e-2 2.0901818181815912e-2 2.6919239669421488e-2 2.9136363636363637e-2 2.3752066115702967e-2 4.853908900000079e-5 5.946769959999995e-4 4.3688600330569024e-4 9.455071044012013e-4 1.3239312405514654e-3 8.175063849737142e-4 3.074909924536329e-2 3.6385865944779515e-2 2.8592068567589057e-2
user_002 Sitting 1.446034577795e12 -0.727487 -0.152682 9.4262 -0.7483890000000002 -0.16313327272727274 9.426199999999998 0.529237335169 2.3311793124000002e-2 88.85324643999999 9.455463794457307 9.45736017391277 2.0902000000000198e-2 1.0451272727272726e-2 1.7763568394002505e-15 2.6919165289256218e-2 1.9002099173553715e-2 2.2801983471075295e-2 4.3689360400000826e-4 1.0922910161983468e-4 3.1554436208840472e-30 1.0315537862246422e-3 4.5014236270323057e-4 1.081182533433542e-3 3.211781104347932e-2 2.121655869134367e-2 3.28813402012987e-2
user_002 Sitting 1.446034578183e12 -0.765807 -0.191003 9.46452 -0.7414216363636363 -0.15268236363636364 9.429683636363636 0.586460361249 3.6482146009e-2 89.5771388304 9.497372338581762 9.460134033566653 2.4385363636363677e-2 3.832063636363636e-2 3.4836363636364e-2 2.7235842975206627e-2 2.8502917355371894e-2 1.9635041322314608e-2 5.94645959677688e-4 1.4684711713140496e-3 1.213572231404984e-3 9.598359052314046e-4 1.2091844044785874e-3 6.509160150263041e-4 3.09812185885482e-2 3.477332892431479e-2 2.5513055775941543e-2
user_002 Sitting 1.446034578766e12 -0.765807 -0.191003 9.4262 -0.7623234545454545 -0.1666170909090909 9.4262 0.586460361249 3.6482146009e-2 88.85324643999999 9.459185427258417 9.45851288519757 3.4835454545455447e-3 2.4385909090909097e-2 0.0 1.7101537190082703e-2 2.501930578512396e-2 2.7552396694215112e-2 1.2135088933884925e-5 5.94672562190083e-4 0.0 4.6778447599248973e-4 8.528350068084148e-4 1.2411534184823567e-3 2.162832577876729e-2 2.9203338966775953e-2 3.523000735853395e-2
user_002 Sitting 1.446034581033e12 -0.727487 -0.191003 9.4262 -0.7623234545454545 -0.17010063636363637 9.478454545454545 0.529237335169 3.6482146009e-2 88.85324643999999 9.456160210211014 9.510648892733103 3.4836454545454476e-2 2.0902363636363636e-2 5.225454545454511e-2 1.741826446280995e-2 2.4068983471074386e-2 2.4702148760330965e-2 1.213578565297516e-3 4.369088055867768e-4 2.730537520661121e-3 4.4682294655447097e-4 1.0150141718414728e-3 1.1650293421487457e-3 2.1138186926850443e-2 3.185928705795961e-2 3.413252616125483e-2
user_002 Sitting 1.446309384445e12 -0.535886 3.2195 9.04299 -0.7309707272727273 0.7809393636363636 9.339108181818183 0.287173804996 10.36518025 81.7756681401 9.613949354718693 9.520764338343959 0.1950847272727273 2.4385606363636363 0.2961181818181835 7.220688429752066e-2 0.7740065371900826 9.595917355371855e-2 3.805805081507439e-2 5.946577977222223 8.768597760330678e-2 8.956297980089407e-3 2.098633624418471 2.3968541014275056e-2 9.4637719647556e-2 1.4486661535421028 0.15481776711435627
user_002 Sitting 1.44630938464e12 -0.574206 3.2195 9.04299 -0.6891668181818181 1.6901753636363637 9.234597272727274 0.329712530436 10.36518025 81.7756681401 9.616161444180104 9.565677478020099 0.11496081818181814 1.5293246363636364 0.19160727272727485 9.627590082644626e-2 1.260769123966942 0.14789826446281007 1.3215989717033047e-2 2.3388338433887688 3.6713346961984285e-2 1.2208727644145751e-2 3.044968591590844 3.636520440157808e-2 0.11049311129724672 1.744983837057193 0.19069662923496597
user_002 Sitting 1.446309385353e12 -0.574206 3.2195 9.15796 -0.5602713636363635 3.2334381818181814 9.098737272727274 0.329712530436 10.36518025 83.86823136159998 9.724357261127132 9.672577064669866 1.3934636363636455e-2 1.3938181818181405e-2 5.9222727272725706e-2 4.877124793388429e-2 0.2900964710743801 5.162198347107379e-2 1.941740905867794e-4 1.942729123966827e-4 3.507331425619649e-3 3.8702471030300487e-3 0.2611054662973247 3.4476748824943267e-3 6.221131008932418e-2 0.5109848004562608 5.871690457180391e-2
user_002 Sitting 1.446309386194e12 -0.574206 3.25783 9.15796 -0.5707223636363637 3.216019090909091 9.154476363636364 0.329712530436 10.613456308899998 83.86823136159998 9.73711457265118 9.719867683131518 3.4836363636362444e-3 4.181090909090868e-2 3.483636363634801e-3 2.2485289256198335e-2 3.674115702479346e-2 2.9135950413221225e-2 1.2135722314048756e-5 1.74815211900823e-3 1.21357223140387e-5 7.138006609226137e-4 1.8670350664162334e-3 1.1142885951163555e-3 2.6717048132655182e-2 4.320920117771484e-2 3.338096156668282e-2
user_002 Sitting 1.446309386519e12 -0.612526 3.2195 9.15796 -0.5776896363636363 3.2125354545454545 9.161443636363638 0.375188100676 10.36518025 83.86823136159998 9.726695210207627 9.725675974401412 3.4836363636363665e-2 6.964545454545501e-3 3.483636363638354e-3 2.2801975206611588e-2 3.674016528925614e-2 2.6919008264462363e-2 1.2135722314049607e-3 4.85048933884304e-5 1.2135722314063454e-5 7.347622479376416e-4 1.7588897474079622e-3 1.2764573379413628e-3 2.7106498260336793e-2 4.1939119535440446e-2 3.572754312769579e-2
user_002 Sitting 1.446309386648e12 -0.574206 3.18118 9.15796 -0.5776896363636363 3.1951163636363633 9.164927272727274 0.329712530436 10.1199061924 83.86823136159998 9.711737747923179 9.72320484422079 3.4836363636363554e-3 1.3936363636363414e-2 6.967272727274931e-3 2.3752057851239683e-2 3.610619834710726e-2 2.6285619834710904e-2 1.213572231404953e-5 1.9422223140495246e-4 4.854288925622906e-5 8.042663787250196e-4 1.7125032538692574e-3 1.2764573379413818e-3 2.8359590595158805e-2 4.1382402707784594e-2 3.5727543127696056e-2
user_002 Sitting 1.44630938775e12 -0.612526 3.2195 9.15796 -0.6090425454545454 3.2299545454545453 9.185829090909092 0.375188100676 10.36518025 83.86823136159998 9.726695210207627 9.756244658044482 3.483454545454623e-3 1.0454545454545272e-2 2.786909090909262e-2 2.2168702479338845e-2 2.217214876033062e-2 2.913586776859457e-2 1.2134455570248473e-5 1.0929752066115321e-4 7.766862280992689e-4 7.612562527084889e-4 8.453236761081932e-4 1.0061617045830013e-3 2.7590872634052167e-2 2.9074450572765656e-2 3.1720052089853214e-2
user_002 Sitting 1.446309387944e12 -0.612526 3.2195 9.19628 -0.6055588181818181 3.2299545454545453 9.178861818181819 0.375188100676 10.36518025 84.57156583839999 9.762783116974175 9.749457085970963 6.9671818181819e-3 1.0454545454545272e-2 1.741818181818111e-2 1.6784818181818206e-2 2.058909090909091e-2 2.6602314049586958e-2 4.8541622487604446e-5 1.0929752066115321e-4 3.0339305785121503e-4 4.1151804822614626e-4 7.051859090909096e-4 8.693590166792054e-4 2.0285907626383055e-2 2.6555336734654857e-2 2.948489472050401e-2
user_002 Sitting 1.446309388852e12 -0.650847 3.2195 9.19628 -0.605558909090909 3.1985981818181823 9.178861818181819 0.42360181740899994 10.36518025 84.57156583839999 9.765262306042219 9.739133143241268 4.528809090909092e-2 2.090181818181769e-2 1.741818181818111e-2 2.1218752066115697e-2 2.09031404958675e-2 3.198611570247953e-2 2.0510111781900835e-3 4.368860033057645e-4 3.0339305785121503e-4 9.432911661134501e-4 5.847724156273373e-4 1.7001043714500528e-3 3.0713045536277416e-2 2.4182068059356243e-2 4.123232192649418e-2
user_002 Sitting 1.446309389111e12 -0.612526 3.06622 9.19628 -0.6020752727272728 3.1776963636363633 9.178861818181817 0.375188100676 9.4017050884 84.57156583839999 9.713313493729933 9.73214500267062 1.0450727272727223e-2 0.11147636363636337 1.7418181818182887e-2 2.5969099173553722e-2 3.388677685950394e-2 2.7869090909091166e-2 1.0921770052892458e-4 1.2426979649586719e-2 3.0339305785127694e-4 1.1209155655725032e-3 1.863416669120946e-3 1.3945048186326265e-3 3.3480077144064396e-2 4.316731019094132e-2 3.734306921816452e-2
user_002 Sitting 1.446309389241e12 -0.574206 3.18118 9.15796 -0.5985916363636363 3.1811800000000003 9.16841090909091 0.329712530436 10.1199061924 83.86823136159998 9.711737747923179 9.723228537958677 2.438563636363633e-2 4.440892098500626e-16 1.0450909090911509e-2 2.8819330578512402e-2 3.1036198347107306e-2 2.6285619834711064e-2 5.946592608595026e-4 1.9721522630525295e-31 1.0922150082649681e-4 1.183801075178814e-3 1.7762370850488212e-3 1.298522287603321e-3 3.4406410379154845e-2 4.214542780716339e-2 3.603501474404196e-2
user_002 Sitting 1.44630938937e12 -0.650847 3.2195 9.15796 -0.605559 3.1881472727272726 9.164927272727274 0.42360181740899994 10.36518025 83.86823136159998 9.72918359519487 9.722676512480279 4.5287999999999995e-2 3.135272727272742e-2 6.967272727274931e-3 3.0402834710743808e-2 3.23028099173553e-2 2.4385454545455234e-2 2.0510029439999994e-3 9.829935074380258e-4 4.854288925622906e-5 1.2533105034477844e-3 1.8512492766340983e-3 1.249979398347126e-3 3.5402125691090705e-2 4.3026146430212624e-2 3.535504770675788e-2
user_002 Sitting 1.446309389629e12 -0.612526 3.2195 9.19628 -0.6125262727272726 3.2020827272727272 9.178861818181819 0.375188100676 10.36518025 84.57156583839999 9.762783116974175 9.740828570831246 2.727272725433494e-7 1.741727272727278e-2 1.741818181818111e-2 2.565241322314048e-2 3.7053966942148756e-2 1.995173553719034e-2 7.438016518893438e-14 3.0336138925620023e-4 3.0339305785121503e-4 1.1727739554079622e-3 2.5872794606310967e-3 5.262490494365031e-4 3.424578741112492e-2 5.086530704351539e-2 2.294011877555352e-2
user_002 Sitting 1.446309390018e12 -0.574206 3.25783 9.15796 -0.5985916363636364 3.2195027272727272 9.171894545454547 0.329712530436 10.613456308899998 83.86823136159998 9.73711457265118 9.739064553708165 2.4385636363636443e-2 3.832727272727254e-2 1.3934545454548086e-2 2.6285809917355386e-2 3.388867768595041e-2 2.058512396694293e-2 5.94659260859508e-4 1.4689798347107296e-3 1.9417155702486672e-4 1.1484991710375648e-3 1.78206255048835e-3 5.615529688955879e-4 3.388951417529565e-2 4.2214482710183125e-2 2.3697108872087917e-2
user_002 Sitting 1.446309391119e12 -0.574206 3.10454 9.15796 -0.5567876363636364 3.1846645454545457 9.144025454545456 0.329712530436 9.638168611600001 83.86823136159998 9.686904175413112 9.698858991586967 1.741836363636362e-2 8.012454545454561e-2 1.3934545454542757e-2 3.293638842975204e-2 2.2486859504132376e-2 1.5201322314048905e-2 3.033993917685945e-4 6.419942784297547e-3 1.9417155702471822e-4 1.478373393021036e-3 1.071374233433505e-3 3.6848465935387405e-4 3.844962149385916e-2 3.273185349828978e-2 1.9195954244420204e-2
user_002 Sitting 1.446309392026e12 -0.535886 3.2195 9.11964 -0.5533039999999999 3.1846645454545457 9.144025454545456 0.287173804996 10.36518025 83.1678337296 9.686082168998775 9.698729922258241 1.7417999999999934e-2 3.4835454545454336e-2 2.4385454545456042e-2 3.515319008264461e-2 3.1037024793388455e-2 4.3070413223140716e-2 3.033867239999977e-4 1.2135088933884152e-3 5.946503933885027e-4 1.567734366244927e-3 1.279874187678435e-3 2.2837222900075043e-3 3.959462547170925e-2 3.577532931614236e-2 4.77883070427014e-2
user_002 Sitting 1.44630939248e12 -0.612526 3.18118 9.15796 -0.5672386363636364 3.163761818181818 9.14054181818182 0.375188100676 10.1199061924 83.86823136159998 9.714078734222612 9.689318632790359 4.528736363636365e-2 1.7418181818182e-2 1.7418181818179335e-2 3.103615702479341e-2 2.1218677685950326e-2 3.0402644628098455e-2 2.050945305132233e-3 3.03393057851246e-4 3.033930578511532e-4 1.2621281915815193e-3 5.747948180315491e-4 1.5489594662659756e-3 3.552644355380256e-2 2.397487889503405e-2 3.9356822359865075e-2
user_002 Sitting 1.446309392932e12 -0.497565 3.14286 9.15796 -0.5672386363636364 3.1672463636363632 9.133574545454547 0.24757092922499999 9.877568979600001 83.86823136159998 9.695017858179787 9.68388161177369 6.967363636363638e-2 2.438636363636304e-2 2.438545454545249e-2 2.3752181818181853e-2 2.8186694214875872e-2 3.325289256198293e-2 4.854415604132234e-3 5.946947314049296e-4 5.946503933883295e-4 9.89626005675433e-4 1.2677851063110273e-3 1.459596420135237e-3 3.1458321723757496e-2 3.5605970093665854e-2 3.8204664900182504e-2
user_002 Sitting 1.446309393711e12 -0.535886 3.14286 9.15796 -0.556787909090909 3.1742136363636364 9.137058181818183 0.287173804996 9.877568979600001 83.86823136159998 9.697060077476884 9.688865473566398 2.0901909090909054e-2 3.1353636363636195e-2 2.0901818181815912e-2 2.7552495867768565e-2 3.452090909090896e-2 2.8502479338842302e-2 4.368898036446266e-4 9.830505132231299e-4 4.3688600330569024e-4 1.119810475468068e-3 1.5546162080390586e-3 1.0547045938392187e-3 3.3463569377280546e-2 3.9428621685763485e-2 3.2476215817721414e-2
user_002 Sitting 1.446309393905e12 -0.574206 3.18118 9.11964 -0.5637551818181818 3.1776972727272725 9.13009090909091 0.329712530436 10.1199061924 83.1678337296 9.67561121854511 9.683824991940147 1.0450818181818144e-2 3.4827272727273595e-3 1.0450909090909732e-2 2.3752148760330553e-2 3.198719008264464e-2 2.2485289256198113e-2 1.0921960066942071e-4 1.2129389256198951e-5 1.092215008264597e-4 9.477042135897816e-4 1.4509074897821168e-3 6.983556567994071e-4 3.07848049139471e-2 3.8090779590107066e-2 2.6426419674246585e-2
user_002 Sitting 1.446309394877e12 -0.574206 3.18118 9.19628 -0.5811733636363636 3.1881472727272726 9.157960000000001 0.329712530436 10.1199061924 84.57156583839999 9.747881029292264 9.714549440349064 6.967363636363633e-3 6.967272727272711e-3 3.83199999999988e-2 2.628568595041322e-2 1.741818181818192e-2 3.2302809917355096e-2 4.854415604132226e-5 4.854288925619812e-5 1.468422399999908e-3 1.1705577291855754e-3 5.174230695717485e-4 1.2047462515401587e-3 3.4213414462540497e-2 2.2746935388569346e-2 3.470945478598243e-2
user_002 Sitting 1.446309396108e12 -0.574206 3.2195 9.15796 -0.5707222727272727 3.1951154545454545 9.130090909090912 0.329712530436 10.36518025 83.86823136159998 9.724357261127132 9.689957950948695 3.4837272727272772e-3 2.4384545454545492e-2 2.786909090908729e-2 2.47022479338843e-2 2.5653553719008248e-2 3.1352727272726776e-2 1.2136355710743833e-5 5.946060570247952e-4 7.766862280989719e-4 1.059130078879039e-3 8.617503026296023e-4 1.2985222876033054e-3 3.254427874264598e-2 2.935558384072104e-2 3.6035014744041735e-2
user_002 Sitting 1.44630939669e12 -0.574206 3.2195 9.11964 -0.5637550909090909 3.2020827272727272 9.130090909090912 0.329712530436 10.36518025 83.1678337296 9.688277788649332 9.69178806671138 1.0450909090909066e-2 1.741727272727278e-2 1.0450909090911509e-2 1.8368264462809904e-2 1.9952644628099234e-2 1.900165289256186e-2 1.0922150082644576e-4 3.0336138925620023e-4 1.0922150082649681e-4 6.023727802885044e-4 5.52808184748308e-4 5.758951861757681e-4 2.4543283812246974e-2 2.3511873271781388e-2 2.3997816279315253e-2
user_002 Sitting 1.446309397792e12 -0.650847 3.18118 9.11964 -0.5811733636363636 3.181180909090909 9.137058181818183 0.42360181740899994 10.1199061924 83.1678337296 9.680461855686897 9.692544633867705 6.967363636363633e-2 9.0909090921798e-7 1.7418181818182887e-2 2.0901900826446305e-2 2.2486611570248005e-2 2.8185785123966575e-2 4.854415604132226e-3 8.264462812227735e-13 3.0339305785127694e-4 9.620433214876044e-4 1.0404994267468033e-3 1.2786638329075584e-3 3.1016823201088863e-2 3.225677334679963e-2 3.575840926142491e-2
user_002 Sitting 1.446309397857e12 -0.574206 3.18118 9.11964 -0.5776897272727273 3.181180909090909 9.14054181818182 0.329712530436 10.1199061924 83.1678337296 9.67561121854511 9.695612912433567 3.4837272727272772e-3 9.0909090921798e-7 2.0901818181819465e-2 1.741827272727274e-2 2.1536528925619927e-2 2.6602314049586472e-2 1.2136355710743833e-5 8.264462812227735e-13 4.368860033058388e-4 8.042789889864763e-4 1.0305684719759548e-3 1.184887796844449e-3 2.835981292227571e-2 3.210246831594036e-2 3.4422199186636075e-2
user_002 Sitting 1.446309398115e12 -0.612526 3.10454 9.11964 -0.584657 3.1776972727272734 9.133574545454548 0.375188100676 9.638168611600001 83.1678337296 9.653040476548103 9.688387501624 2.7869000000000033e-2 7.315727272727335e-2 1.3934545454548086e-2 3.008621487603306e-2 2.407008264462823e-2 2.4385454545455234e-2 7.766811610000018e-4 5.351986552892653e-3 1.9417155702486672e-4 1.797227750449286e-3 1.3549278384673222e-3 8.550167993989645e-4 4.239372300764921e-2 3.680934444495476e-2 2.924067029667693e-2
user_002 Sitting 1.446309398569e12 -0.612526 3.2195 9.11964 -0.5951078181818181 3.1846636363636365 9.109188181818183 0.375188100676 10.36518025 83.1678337296 9.690624442226413 9.668323338838917 1.7418181818181888e-2 3.4836363636363554e-2 1.0451818181817174e-2 2.786923966942151e-2 3.1036363636363692e-2 2.945347107438097e-2 3.033930578512421e-4 1.213572231404953e-3 1.0924050330576405e-4 1.326128349746056e-3 1.646059640571004e-3 1.2214061022539973e-3 3.6416045223857794e-2 4.057166055969368e-2 3.494862089201801e-2
user_002 Sitting 1.446309399282e12 -0.497565 3.2195 9.11964 -0.563755 3.198599090909091 9.119639090909093 0.24757092922499999 10.36518025 83.1678337296 9.684037634624568 9.680833551221772 6.619000000000003e-2 2.0900909090908915e-2 9.090909074416231e-7 2.5969000000000016e-2 1.7419008264462865e-2 2.565413223140357e-2 4.381116100000004e-3 4.368480008264389e-4 8.264462779930337e-13 1.1915174160338085e-3 5.52832369797143e-4 1.0603619127722878e-3 3.451836346111745e-2 2.3512387581807657e-2 3.256319874908311e-2
user_002 Sitting 1.446309399346e12 -0.574206 3.18118 9.08132 -0.563755 3.198599090909091 9.123123636363637 0.329712530436 10.1199061924 82.47037294239999 9.639501629505334 9.684115539772451 1.0450999999999988e-2 1.7419090909091217e-2 4.180363636363715e-2 2.501892561983473e-2 1.8685867768595103e-2 2.4069917355370472e-2 1.0922340099999975e-4 3.034247280991843e-4 1.7475440132232066e-3 1.1617299067332827e-3 5.793131885048824e-4 9.003029230652933e-4 3.40841591759762e-2 2.4068925786268118e-2 3.000504829300052e-2
user_002 Sitting 1.446309399411e12 -0.574206 3.2195 9.19628 -0.5672386363636365 3.2020827272727272 9.13009090909091 0.329712530436 10.36518025 84.57156583839999 9.760453812135786 9.692028365975302 6.967363636363522e-3 1.741727272727278e-2 6.618909090908964e-2 2.1218611570247944e-2 1.995256198347112e-2 2.8820165289254716e-2 4.8544156041320715e-5 3.0336138925620023e-4 4.380995755371733e-3 9.49907311271224e-4 6.057882491359869e-4 1.2809186979713656e-3 3.0820566368436903e-2 2.4612765978979018e-2 3.578992453151258e-2
user_002 Sitting 1.446309399929e12 -0.574206 3.14286 9.08132 -0.5672386363636365 3.195115454545454 9.109189090909092 0.329712530436 9.877568979600001 82.47037294239999 9.626923415735476 9.670031425217148 6.967363636363522e-3 5.225545454545388e-2 2.786909090909262e-2 1.3301322314049503e-2 2.7553388429752038e-2 2.94526446280997e-2 4.8544156041320715e-5 2.730632529751997e-3 7.766862280992689e-4 4.5896321775356784e-4 1.0139892420736236e-3 1.2610118732532096e-3 2.142342684431153e-2 3.18431977363082e-2 3.5510728987915886e-2
user_002 Sitting 1.446309400059e12 -0.574206 3.18118 9.11964 -0.5742060000000001 3.195115454545454 9.116156363636366 0.329712530436 10.1199061924 83.1678337296 9.67561121854511 9.676979535721001 1.1102230246251565e-16 1.3935454545454196e-2 3.483636363634801e-3 6.3339586776858855e-3 2.7553388429752e-2 3.0085950413223535e-2 1.232595164407831e-32 1.9419689338842001e-4 1.21357223140387e-5 5.075053584447656e-5 1.0184010803906773e-3 1.2896963077385455e-3 7.123941033197605e-3 3.191239697031042e-2 3.5912341997404534e-2
user_002 Standing 1.446034733761e12 -1.45557 -9.4262 -5.99e-4 -1.46515 -9.40704 0.1718425 2.1186840249000003 88.85324643999999 3.5880100000000004e-7 9.537920676106559 9.522599287107857 9.579999999999922e-3 1.91599999999994e-2 0.1724415 1.0378333333333323e-2 4.470666666666645e-2 5.7480375e-2 9.177639999999851e-5 3.67105599999977e-4 2.973607092225e-2 1.5551001111111117e-4 5.119083644444456e-3 7.8928997305625e-3 1.2470365315864294e-2 7.154777176435655e-2 8.884199305825202e-2
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user_003 Jogging 1.446047740033e12 -3.71647 -18.85299 0.497565 -4.106641636363637 -8.123307272727272 -0.9168033636363636 13.812149260900002 355.4352319400999 0.24757092922499999 19.22225148441839 10.77016093587484 0.39017163636363694 10.729682727272726 1.4143683636363635 1.899864553719008 6.932174727272727 1.5011428016528925 0.15223390582267815 115.12609142793468 2.0004378680554047 5.325225943114908 67.17508940760895 3.137830390156627 2.3076451077050186 8.19604108137636 1.771392218046762
user_003 Jogging 1.446047740163e12 -7.28026 -6.20729 -1.34181 -4.381851636363636 -9.060413636363636 -0.8610647272727273 53.0021856676 38.530449144100004 1.8004540760999999 9.660905179526399 11.655872111868048 2.8984083636363644 2.8531236363636356 0.48074527272727263 2.1592396776859504 7.111743074380166 1.624021338842975 8.400771042397228 8.140314484376855 0.23111601724961975 6.355301068903384 68.16794305933205 3.3226541962235387 2.5209722467538955 8.256388015308634 1.8228149100288649
user_003 Jogging 1.446047741586e12 -5.70913 -13.79471 2.18366 -4.754604272727273 -8.084986727272726 -0.526633 32.5941653569 190.2940239841 4.768370995600001 15.088292161030022 11.192019763213258 0.9545257272727268 5.709723272727274 2.710293 2.1820410909090913 7.525347834710744 1.5670159504132235 0.911119364025528 32.60093985112345 7.345688145849 6.725637535457142 70.61233436629162 3.209251785542351 2.593383414664546 8.403114563439654 1.7914384682545899
user_003 Jogging 1.446047741846e12 -4.78944 -17.01362 1.26397 -4.639642454545454 -8.078019545454545 -0.5161817272727273 22.938735513599998 289.4632655044 1.5976201609 17.720034457610403 10.869660757908436 0.14979754545454593 8.935600454545455 1.7801517272727274 2.1741234710743806 7.074687818181817 1.5527638429752066 2.2439304624206756e-2 79.84495548327294 3.168940172112075 6.7387556156140995 62.02374722341651 3.395613878513215 2.595911326608461 7.875515679840686 1.8427191534558962
user_003 Jogging 1.446047741911e12 -9.92436 -19.08292 -5.13552 -4.942721545454545 -8.123307727272728 -0.7461035454545454 98.4929214096 364.15783572640004 26.373565670399998 22.113894338320424 11.071813299428175 4.981638454545455 10.959612272727274 4.389416454545454 2.4198804876033058 7.12631 1.7234634462809917 24.816721691806027 120.11310116851428 19.266976811434386 8.522939200738632 63.12595207200314 4.573635273326528 2.9194073372413505 7.945184206297745 2.1386059181921593
user_003 Jogging 1.446047742105e12 -1.37893 1.03525 -3.71767 -5.291088181818181 -8.461222363636365 -1.038731181818182 1.9014479449 1.0717425625 13.8210702289 4.09808012809657 11.394511324828654 3.912158181818181 9.496472363636364 2.678938818181818 2.4556680578512395 7.01831676859504 1.8542590495867766 15.304981639566938 90.18298735330924 7.1767131915613955 7.66219816374371 59.86598085424357 4.899174334712138 2.7680675865563162 7.737310957577159 2.213407855482613
user_003 Jogging 1.446047743076e12 -8.27659 -15.05928 -0.728685 -4.587387272727272 -9.088283272727274 0.2606753636363636 68.5019420281 226.78191411839998 0.530981829225 17.19926853025224 11.999853736250367 3.689202727272728 5.970996727272725 0.9893603636363637 3.0143207438016533 7.571903148760328 1.6436561157024796 13.610216762916535 35.65280191710159 0.9788339291346778 13.052084914282272 67.81846212605052 3.7920228341500035 3.612766933291196 8.235196544469993 1.9473116941440072
user_003 Jogging 1.44604774327e12 -2.29862 -1.18733 1.30229 -4.639641818181818 -8.698112363636362 -2.150190909090909e-2 5.2836539044 1.4097525289 1.6959592440999998 2.8964401732816785 11.391576321113966 2.3410218181818183 7.510782363636362 1.323791909090909 2.8230356198347106 7.835078702479337 1.5758826859504131 5.480383153203307 56.41185171391101 1.7524250185745534 12.127020067467846 69.08815603044107 2.9333404785628705 3.4823871219994835 8.311928538578822 1.7126997631116991
user_003 Jogging 1.446047743659e12 -6.28393 -8.54483 -3.90927 -4.674479090909092 -8.569216363636365 -0.5161813636363636 39.4877762449 73.01411972889998 15.282391932899998 11.304171261384 11.09202422756434 1.6094509090909082 2.438636363636526e-2 3.393088636363636 2.6973064462809915 7.171282801652893 1.653155925619835 2.590332228773551 5.946947314050379e-4 11.513050494220039 11.415731180268821 63.780162821143975 3.500501430448313 3.3787173868598157 7.9862483570913305 1.8709627015117947
user_003 Jogging 1.446047744112e12 -6.32225 -19.58108 -2.2615 -4.158896818181819 -8.503027454545455 -0.5684371818181818 39.970845062500004 383.4186939664 5.114382249999999 20.700336260044182 11.354514333727545 2.1633531818181817 11.078052545454545 1.6930628181818181 2.7714127272727276 6.852686305785125 1.8821283719008262 4.680096989282851 122.72324819985192 2.86646170630976 12.191477094626935 62.46514659401501 5.505646912405573 3.4916295758036724 7.903489520080039 2.346411496819254
user_003 Jogging 1.446047745795e12 -1.11069 0.958607 -2.68302 -3.9951649999999996 -9.670054818181818 -9.465881818181819e-2 1.2336322760999998 0.918927380449 7.1985963204 3.0579659868855638 11.578644378470724 2.8844749999999997 10.628661818181818 2.5883611818181818 2.4385655123966945 6.973345719008264 1.5590983388429753 8.320196025624998 112.96845204527604 6.699613607543214 8.35464690663406 56.06450086026842 3.6200956105588475 2.8904406076987743 7.487623178303541 1.9026548847751785
user_003 Jogging 1.446047746378e12 -8.23827 -17.32018 -1.26517 -4.576936636363637 -9.276400272727273 -0.4743760909090911 67.8690925929 299.98863523240004 1.6006551288999997 19.221300240987862 11.717208326426968 3.6613333636363627 8.043779727272728 0.7907939090909089 2.3983437355371895 6.6256129008264475 2.0360425371900828 13.405361999676762 64.70239230088373 0.6253550066552807 7.549598737169998 57.38207630334404 5.904934442457743 2.747653314588651 7.575095794994545 2.4300070869151273
user_003 Jogging 1.446047746443e12 -1.53221 -8.12331 1.72382 -4.806858181818182 -9.607348454545455 -0.282774090909091 2.3476674841 65.9881653561 2.9715553923999996 8.4443702093525 12.065932595475562 3.274648181818182 1.4840384545454555 2.0065940909090907 2.191540991735537 6.272179206611571 2.185207082644628 10.723320714685125 2.202370134569664 4.02641984567128 5.724745155916998 54.95898877838006 6.258809155594935 2.3926439676468787 7.413432995473828 2.5017612107463285
user_003 Jogging 1.446047747867e12 -8.54483 -16.05561 -3.25783 -4.4793936363636355 -8.879263090909092 -0.8645490000000001 73.01411972889998 257.7826124721 10.613456308899998 18.477288451228443 11.952809629959383 4.065436363636364 7.17634690909091 2.3932809999999995 2.48765438016529 7.61592423140496 1.7449996942148758 16.52777282677686 51.499954959618655 5.727793944960998 9.127936903276487 72.93491111289995 4.231126364306643 3.0212475739794127 8.540193856868822 2.056970190427329
user_003 Jogging 1.446047749615e12 -5.24928 -13.29655 1.22565 -4.2076685454545455 -8.370647363636364 -0.29670981818181813 27.5549405184 176.7982419025 1.5022179224999999 14.347661842383935 11.022203270846463 1.0416114545454542 4.925902636363636 1.522359818181818 1.9812563471074378 7.141195123966941 1.5100093719008265 1.084954422240297 24.264516782934223 2.317579416014578 6.159065103561868 61.365181331507394 3.5171502368635177 2.4817463817968726 7.833593130327065 1.8754066857253968
user_003 Jogging 1.446047750068e12 -8.12331 -17.09026 -4.40743 -4.510747636363636 -8.475158181818182 -0.7251994545454544 65.9881653561 292.0769868676 19.425439204899998 19.429117103682298 11.165998374535848 3.612562363636364 8.615101818181818 3.682230545454545 2.161772330578512 7.3682685950413225 1.7811014214876033 13.050606831161954 74.21997933763967 13.558821789878477 6.444378643861114 63.33591248530026 3.728135679427015 2.5385780751950717 7.958386299074723 1.9308380769570024
user_003 Jogging 1.446047750974e12 3.8919e-2 -0.842448 -1.57173 -3.8732365454545454 -9.973134363636364 -0.40122081818181826 1.514688561e-3 0.7097186327039999 2.4703351929000004 1.7836951853287601 11.766917856584998 3.9121555454545454 9.130686363636364 1.1705091818181819 2.1823563719008265 6.663935347107437 1.389666223140496 15.304961011830752 83.36943347109505 1.3700917447206695 6.276925041612132 57.1699286394013 3.746889708828522 2.5053792211184582 7.561079859345575 1.9356884327878086
user_003 Jogging 1.446047751169e12 -2.6435 -19.58108 2.10702 -3.7025366363636367 -8.384583090909091 -0.17478227272727276 6.98809225 383.4186939664 4.439533280399999 19.870740285575675 10.519545204986324 1.0590366363636368 11.196496909090909 2.2818022727272727 1.7560833388429749 6.586661157024793 1.5315473223140499 1.1215585971604058 125.36154303528228 5.206621611823347 4.519674473767474 57.41535496920656 4.058250858479553 2.1259526038384475 7.577292060439967 2.0145100790215853
user_003 Jogging 1.446047751428e12 -4.02303 -2.79678 1.41725 -4.137994636363636 -8.785204 -0.44999136363636366 16.1847703809 7.8219783684 2.0085975625 5.100524121284008 10.925348616610346 0.11496463636363607 5.988424 1.8672413636363636 1.6297226611570246 7.185217322314048 1.6297223140495867 1.3216867614223074e-2 35.861222003776 3.4865903100745865 5.189255505654557 62.7452396789755 3.459631785679336 2.277993745745268 7.921189284379935 1.86000854451783
user_003 Jumping 1.446047778488e12 0.805325 -10.92069 -1.49509 -3.045865625 -10.45605625 -2.8985725 0.6485483556249999 119.26147007610001 2.2352941081 11.051937049215626 11.40789343159099 3.8511906249999996 0.46463375000000084 1.4034825000000002 1.2694057180059524 2.5898877395833337 0.9794885 14.831669230087888 0.2158845216390633 1.9697631278062506 2.994031096828895 19.251323506625305 2.225648644605465 1.7303268757170984 4.387633018681633 1.491860799339357
user_003 Jumping 1.446047779394e12 -3.75479 -19.19788 -4.9056 -2.7758821818181816 -10.80573090909091 -2.442647 14.098447944099998 368.55859649440004 24.064911359999996 20.167348754819013 11.820595137903576 0.9789078181818183 8.392149090909092 2.4629529999999997 1.600585561983471 5.376877752066116 1.2062982314049586 0.9582605164974878 70.42816636404629 6.066137480208998 3.2206154865366234 39.98863645901631 1.938698124881656 1.7946073349166451 6.323656889728942 1.3923714033553174
user_003 Jumping 1.446047779718e12 -0.574206 -0.535886 -1.18853 -2.692273545454545 -6.2699988181818185 -1.8852610909090906 0.329712530436 0.287173804996 1.4126035609000003 1.4246016623365285 7.945104724247008 2.1180675454545446 5.734112818181819 0.6967310909090905 1.9156986446280988 6.127132917355372 1.4292522892561985 4.48621012710784 32.88004981163704 0.4854342130393713 4.538447186411323 48.73007696745106 2.676119181954217 2.130363158339752 6.980693158093333 1.6358848315068566
user_003 Jumping 1.446047779783e12 -1.72382 -13.98632 -4.10087 -2.5633780909090906 -7.144398818181816 -2.104732 2.9715553923999996 195.61714714239997 16.817134756899996 14.676710710908626 8.766751727191796 0.8395580909090907 6.841921181818183 1.9961379999999997 1.8707269752066111 6.4061433140495865 1.5936175289256198 0.704857788010917 46.81188545821232 3.984566915043999 4.440687567006215 51.69169643753226 3.035135331393246 2.107293896685086 7.189693765212275 1.7421639794787533
user_003 Jumping 1.446047779847e12 -3.14167 -19.58108 -3.48775 -2.5424762727272725 -8.530896999999998 -2.1987910909090904 9.8700903889 383.4186939664 12.1644000625 20.135868106883297 10.050840976414916 0.5991937272727275 11.050183000000002 1.2889589090909097 1.7627335867768592 7.189334537190083 1.6230705206611569 0.3590331228029837 122.10654433348905 1.661415069324828 4.182981353748214 62.25323570487753 3.1015204576431388 2.0452338139558064 7.890071970830021 1.7611134141909028
user_003 Jumping 1.446047780236e12 -4.02303 -9.84772 -0.383802 -2.0791488181818183 -7.405672454545454 -1.9200985454545454 16.1847703809 96.97758919840001 0.147303975204 10.644701196111802 8.261996395467271 1.943881181818182 2.442047545454547 1.5362965454545454 1.4647220413223139 4.597488347107438 1.317141173553719 3.778674049026852 5.963596214260577 2.36020707557557 2.7032977327714196 31.28153946209859 2.150969664053501 1.6441708344242758 5.5929902075811455 1.4666184452861286
user_003 Jumping 1.446047780559e12 -1.8771 1.99325 -1.68669 -2.995352090909091 -8.844426363636364 -2.5123207272727273 3.52350441 3.9730455625 2.8449231561 3.215816090605929 10.297818465970156 1.118252090909091 10.837676363636364 0.8256307272727272 1.4400184710743802 4.84324438016529 1.320624966942149 1.2504877388225537 117.45522896292232 0.6816660978168925 2.8856324564354807 37.52954362327869 2.3031833074215906 1.6987149426656258 6.126136108778411 1.5176242312975865
user_003 Jumping 1.446047782114e12 -3.02671 -6.93538 -2.68302 -2.1592739090909094 -9.077831363636363 -2.784047363636363 9.1609734241 48.0994957444 7.1985963204 8.028640326288132 10.440987932571106 0.8674360909090906 2.142451363636363 0.101027363636363 1.4593388842975203 6.418493917355372 1.5176108347107438 0.7524453718116441 4.590097845547312 1.020652820331392e-2 3.096061633576934 52.39564747111347 2.9478029008267157 1.7595629098094032 7.23848378261038 1.7169166842997117
user_003 Jumping 1.446047783021e12 -1.76214 -12.22358 -5.67201 -2.2951368181818177 -8.046666363636364 -2.6028974545454546 3.1051373796000004 149.4159080164 32.171697440100004 13.590170817031698 9.340850426104161 0.5329968181818177 4.176913636363636 3.0691125454545456 1.147392132231405 5.408547049586778 1.5980530743801653 0.28408560819194156 17.446607525640495 9.41945181666648 2.104757384422643 39.50631767277085 3.717980372110848 1.450778199595873 6.285405131952183 1.9282065169765525
user_003 Jumping 1.446047783474e12 -2.8351 -4.63616 -3.75599 -1.9258677272727274 -6.823900909090909 -2.5610926363636364 8.03779201 21.493979545600002 14.107460880100001 6.6059997302225195 8.171110182376047 0.9092322727272728 2.187740909090909 1.1948973636363638 1.018495512396694 4.917666958677686 1.2648870661157026 0.8267033257688018 4.786210285309917 1.4277797096251326 1.6454297082086164 35.01551621607166 2.5264965598920623 1.2827430406003442 5.917390997396713 1.589495693574557
user_003 Jumping 1.446047783928e12 -1.22565 0.345482 -0.805325 -2.3752596363636367 -6.256064 -2.17789 1.5022179224999999 0.119357812324 0.6485483556249999 1.5066930976310338 7.873185761106638 1.1496096363636368 6.601546 1.3725650000000003 1.3497614297520661 5.791750727272727 1.7095292975206613 1.3216023160201331 43.580409590116 1.8839346792250007 2.7612193103155254 44.96614526686418 5.186450031648668 1.6616917013440025 6.705680074896518 2.2773778851232986
user_003 Jumping 1.446047785158e12 -4.3296 -19.38948 -5.17384 -2.127920545454545 -8.778236090909092 -3.0174524545454546 18.74543616 375.95193467039996 26.768620345600002 20.529636898299003 10.425059342349634 2.201679454545455 10.611243909090907 2.1563875454545456 1.4099344958677689 7.0499873553719 1.8989135371900827 4.847392420567572 112.59849729821889 4.65000724619148 2.826879506975875 61.40943646769882 5.966533630196475 1.6813326580352488 7.836417323477535 2.442648896218299
user_003 Jumping 1.446047785741e12 -5.67081 -19.58108 -6.59169 -2.981417909090909 -11.300410000000001 -3.0104854545454547 32.158086056100004 383.4186939664 43.450377056099995 21.424919068192533 12.213006242934197 2.689392090909091 8.280669999999999 3.581204545454545 1.1746283057851243 4.157596 1.0412976611570246 7.232829818644373 68.56949564889999 12.825025996384296 1.990508293795564 32.482416710883314 2.1246119344821945 1.4108537464229112 5.699334760380664 1.457604862259383
user_003 Jumping 1.446047786065e12 -3.7722e-2 0.230521 0.382604 -2.6016978181818184 -7.217555818181818 -2.3207198181818183 1.422949284e-3 5.3139931441e-2 0.146385820816 0.4482730212058272 8.746920955704528 2.5639758181818184 7.448076818181819 2.7033238181818184 1.274704181818182 5.073483123966943 1.6246536198347108 6.573971996221125 55.4738482895374 7.3079596659491255 2.612508774391919 37.036034654309766 4.703861187725261 1.6163257018286628 6.085723839799976 2.1688386725907627
user_003 Jumping 1.44604778697e12 -0.267643 -8.92803 -1.57173 -2.608665363636364 -10.115963636363636 -3.3309809090909095 7.163277544900001e-2 79.7097196809 2.4703351929000004 9.069271616246201 11.16523610158163 2.341022363636364 1.1879336363636366 1.7592509090909094 1.3396285206611571 3.1194631487603317 1.5305941487603305 5.4803857070455875 1.4111863244041327 3.0949637611371914 2.725388990184014 16.98034189431018 4.198812068786995 1.6508752194469496 4.120721040583818 2.0491003071560443
user_003 Jumping 1.446047787165e12 -0.650847 0.383802 -0.728685 -2.3682926363636363 -7.3185804545454545 -2.703921636363636 0.42360181740899994 0.147303975204 0.530981829225 1.049708350847034 9.016998308071146 1.7174456363636363 7.702382454545455 1.9752366363636358 1.3750980991735537 5.015211049586777 1.9258318429752064 2.9496195138644956 59.32669547608966 3.90155976963313 3.0779925111574262 38.28173155279879 5.6355475934485995 1.7544208477892145 6.187223250602712 2.373930831647923
user_003 Jumping 1.446047788071e12 -0.382604 -7.1653 -1.83997 -2.674855818181818 -10.45388 -3.4598772727272733 0.146385820816 51.34152409 3.3854896009 7.407658166500125 11.447674154518019 2.2922518181818177 3.2885799999999996 1.6199072727272732 0.9424898099173553 3.4890507603305783 1.4162686033057852 5.254418397957849 10.814758416399998 2.6240995722347122 1.5625571828485925 19.114791200640433 3.1594544490391656 1.2500228729301686 4.372046568901163 1.7774854286432746
user_003 Jumping 1.446047788524e12 -1.83878 -13.06663 -4.40743 -2.284686363636364 -9.189309181818182 -3.341432 3.3811118884000004 170.7368195569 19.425439204899998 13.911986581728721 10.958216505306934 0.4459063636363638 3.8773208181818184 1.0659979999999996 1.2341684628099174 7.045554041322314 2.3818761983471077 0.1988324851314051 15.033616727106125 1.136351736003999 2.4039647392245826 56.751996420586586 6.585076787756369 1.5504724245289185 7.533392092582636 2.566140445836192
user_003 Jumping 1.446047788978e12 -4.98104 -15.97897 -4.67568 -2.476287272727273 -9.502837545454547 -3.463361818181818 24.8107594816 255.3274822609 21.861983462399998 17.37815367652444 10.622998855950827 2.5047527272727272 6.4761324545454535 1.2123181818181816 0.6900824132231407 3.6885678677685947 1.235749785123967 6.2737862247801655 41.94029156881692 1.4697153739669417 0.9094025823986598 24.75910834947861 2.8048255856699282 0.9536260181007331 4.975852524892454 1.6747613518558184
user_003 Jumping 1.446047789366e12 -0.689167 0.230521 -0.728685 -2.040828272727273 -7.03640390909091 -2.648185181818182 0.47495115388899994 5.3139931441e-2 0.530981829225 1.029112683118326 8.566401817896816 1.3516612727272732 7.2669249090909105 1.919500181818182 0.9640250082644628 5.1925611652892565 1.7240976033057849 1.826988196190712 52.80819763436594 3.684480948000034 1.8265146617737733 38.92138095737842 4.682598069418348 1.3514860938144253 6.238700261863718 2.163931160970318
user_003 Jumping 1.446047789431e12 -1.14901 -1.95374 -2.72134 -1.953736454545455 -6.5486911818181825 -2.7039233636363638 1.3202239801000002 3.8170999876000002 7.405691395600001 3.5416119724357156 8.169979126377969 0.8047264545454549 4.594951181818183 1.741663636363633e-2 1.0083625371900826 5.557712355371901 1.6746931487603307 0.647584666645298 21.113576363292314 3.0333922222313927e-4 1.8762498455014827 40.81039543439705 4.654028349160952 1.3697626967841847 6.388301451434258 2.1573197141733425
user_003 Jumping 1.446047789495e12 -3.90807 -17.74171 -7.58802 -2.1139846363636363 -7.62514390909091 -3.205570636363637 15.2730111249 314.7682737241 57.578047520400006 19.688050496923253 9.358800088769957 1.7940853636363636 10.116566090909092 4.382449363636363 1.1537262148760332 6.411527363636364 2.0167259669421482 3.2187422920142232 102.34490947173167 19.205862424836763 2.1654029518886837 50.06674660371802 6.36506042608091 1.4715308192113015 7.0757859354080255 2.5229071378235286
user_003 Jumping 1.44604778969e12 -2.79678 -7.7401 -2.37646 -2.023410090909091 -8.565733909090909 -3.4076233636363638 7.8219783684 59.90914801 5.647562131599999 8.566136148229258 10.261278348407382 0.773369909090909 0.8256339090909091 1.031163363636364 1.00804579338843 6.803598520661157 2.0537784710743803 0.5981010162872809 0.6816713518407355 1.06329788250586 1.7002829353981377 55.666831209060064 6.432113881496044 1.303948977298628 7.46102078867631 2.5361612491117445
user_003 Jumping 1.446047790078e12 -5.51753 -19.58108 -7.24314 -2.786332727272727 -10.19608909090909 -3.6131590909090905 30.4431373009 383.4186939664 52.4630770596 21.594557377424987 11.293414580744383 2.7311972727272726 9.38499090909091 3.62998090909091 0.8785175041322314 4.163930198347109 1.2959231239669422 7.459438542552892 88.07805436371902 13.176761400364468 1.3735754555330413 30.66790812930183 3.5983363200454987 1.171996354743922 5.537861331714783 1.8969281272745941
user_003 Jumping 1.446047790984e12 -3.94639 -5.36425 -3.75599 -2.120953181818182 -7.109561 -3.2508581818181814 15.5739940321 28.7751780625 14.107460880100001 7.645693753656368 8.673083640943078 1.8254368181818181 1.745311 0.5051318181818187 1.195847074380165 4.592418834710744 1.636056132231405 3.33221957717376 3.046110486721 0.25515815373967 2.4076508899487554 32.64328227998147 4.830573809957643 1.551660687762874 5.713429992568516 2.1978566399921635
user_003 Jumping 1.446047791114e12 -7.70178 -19.58108 -7.5497 -2.946581363636364 -10.105513 -4.309891818181819 59.317415168400004 383.4186939664 56.997970089999995 22.354732814882848 11.61773381092931 4.7551986363636365 9.475567 3.239808181818181 1.3019401157024795 4.772619710743801 1.4381207768595041 22.611914071274587 89.786369971489 10.496357054976027 3.343503517246846 35.837988853437764 4.02036337652106 1.8285249566923734 5.9864838472543935 2.0050843813967183
user_003 Jumping 1.446047791568e12 -2.87342 -15.97897 -6.28513 -2.3055863636363636 -6.6601691818181825 -3.212538181818182 8.2565424964 255.3274822609 39.5028591169 17.409390680727455 8.421526987651102 0.5678336363636363 9.318800818181817 3.0725918181818175 1.446669702479339 6.484367231404959 2.031925909090909 0.3224350385859503 86.8400486889461 9.440820481157846 3.813957346986096 49.52847432526871 5.995280938105451 1.9529355716423664 7.037646930989697 2.448526278826807
user_003 Jumping 1.446047791827e12 -2.29862 -6.55217 -2.49142 -1.9641881818181817 -7.280260090909092 -3.181184545454545 5.2836539044 42.930931708900005 6.207173616400001 7.377110493255472 8.788531724429772 0.33443181818181844 0.7280900909090917 0.6897645454545449 1.1261739999999998 6.306384099173553 2.2213108677685947 0.11184464101239687 0.5301151804800094 0.47577512816611495 1.9109248881675382 50.99588928979224 6.629910003092078 1.3823620684059361 7.141140615461387 2.5748611619060315
user_003 Jumping 1.446047792344e12 -3.10335 3.14286 -1.26517 -2.953548181818182 -8.90713090909091 -3.501681181818181 9.6307812225 9.877568979600001 1.6006551288999997 4.594453757629953 10.941628346937778 0.14980181818181793 12.04999090909091 2.236511181818181 0.999812826446281 3.8237974793388427 1.812455851239669 2.2440584730578434e-2 145.2022809091736 5.001982266397757 1.8885143120312426 26.270304023665425 5.8452978576593555 1.374232262767558 5.12545646978544 2.4177050807861895
user_003 Jumping 1.446047793057e12 -3.40991 -4.5212 -3.18118 -2.462351909090909 -7.2071046363636375 -3.024419818181818 11.6274862081 20.441249440000004 10.1199061924 6.495278426711207 8.674293689934707 0.9475580909090908 2.685904636363637 0.15676018181818208 1.0726530165289256 4.93793579338843 1.4678901570247935 0.8978663356472808 7.214083715639682 2.4573754603669503e-2 1.72976303665992 39.52732881159241 3.1747400768519607 1.3152045607660885 6.287076332572431 1.7817800304336
user_003 Jumping 1.446047793186e12 -4.7128 -14.7144 -2.75966 -3.2113400000000003 -8.840943 -3.634060909090908 22.21048384 216.51356736 7.615723315599999 15.695215019731332 10.612367757126883 1.5014599999999994 5.873457 0.8744009090909084 0.7952270578512397 4.540798404958678 1.071702603305785 2.254382131599998 34.497497130849 0.764576949819007 0.7830567086205332 34.99927923490504 1.741114685615601 0.8849049150165984 5.916018867017332 1.3195130486719717
user_003 Jumping 1.446047793575e12 -0.995729 0.383802 -0.537083 -2.7410467272727272 -6.395409181818182 -2.8885566363636364 0.991476241441 0.147303975204 0.28845814888899995 1.1946708189011732 8.27717575135295 1.7453177272727274 6.779211181818182 2.3514736363636364 1.2639381239669418 5.466502917355373 1.8156223140495868 3.0461339691324385 45.957704247688675 5.529428262513223 1.9598808640562646 39.03616815904957 4.99167780265026 1.3999574508020822 6.247893097600948 2.2342063026162693
user_003 Jumping 1.446047794481e12 -1.95374 3.41111 -1.07357 -2.643502818181818 -9.126602727272727 -3.428524545454545 3.8170999876000002 11.635671432099999 1.1525525448999998 4.0749630629737 10.79227622301754 0.6897628181818181 12.537712727272726 2.354954545454545 1.1131894545454544 3.9501590082644626 1.6290873471074379 0.4757727453461238 157.19424043161652 5.545810911157022 1.8705564207425525 31.301814921364322 3.736381640676486 1.3676828655585886 5.594802491720715 1.932972229670278
user_003 Sitting 1.44604752743e12 0.460442 -0.689167 9.38788 0.46044236363636365 -0.657814 9.443618181818183 0.21200683536400003 0.47495115388899994 88.13229089439999 9.424396473178163 9.478071981030691 3.6363636363168084e-7 3.1352999999999964e-2 5.573818181818346e-2 3.4032538370720185e-2 4.40547175127902e-2 2.419795146267877e-2 1.3223140495527202e-13 9.830106089999977e-4 3.1067449123968775e-3 2.3483069980241396e-3 3.906631446102497e-3 8.135460878653428e-4 4.845933344593319e-2 6.250305149432703e-2 2.8522729320058816e-2
user_003 Sitting 1.446047527559e12 0.460442 -0.612526 9.50284 0.453475 -0.6578139090909091 9.44710181818182 0.21200683536400003 0.375188100676 90.30396806560002 9.53368569870226 9.481220909788886 6.967000000000001e-3 4.528790909090907e-2 5.573818181818169e-2 3.4032455037386854e-2 5.070537866981499e-2 2.7628805457168906e-2 4.8539089000000014e-5 2.0509947098264446e-3 3.1067449123966797e-3 2.308586652947751e-3 4.1636947314954344e-3 1.065423617408702e-3 4.804775388036106e-2 6.452669781954935e-2 3.264082746207121e-2
user_003 Sitting 1.446047528402e12 0.422122 -0.689167 9.46452 0.4569586363636363 -0.6752324545454544 9.457552727272725 0.178186982884 0.47495115388899994 89.5771388304 9.498961888920968 9.492741447006507 3.483663636363632e-2 1.3934545454545533e-2 6.967272727274931e-3 3.166966115702479e-2 2.5652355371900804e-2 2.565223140495896e-2 1.2135912331322283e-3 1.9417155702479557e-4 4.854288925622906e-5 1.4210099365206607e-3 7.910343762411707e-4 1.09331825574758e-3 3.769628544725144e-2 2.8125333353423043e-2 3.3065363384478026e-2
user_003 Sitting 1.446047529049e12 0.460442 -0.650847 9.46452 0.4639258181818182 -0.657814 9.436650909090908 0.21200683536400003 0.42360181740899994 89.5771388304 9.49803913885245 9.471062812864579 3.483818181818199e-3 6.9670000000000565e-3 2.786909090909262e-2 2.0901991735537175e-2 3.3886504132231404e-2 2.565223140495896e-2 1.2136989123967062e-5 4.853908900000079e-5 7.766862280992689e-4 1.0150072620518401e-3 1.7045471308392188e-3 1.0182974268970488e-3 3.1859178615460886e-2 4.128616149315917e-2 3.191077289720587e-2
user_003 Sitting 1.446047529689e12 0.383802 -0.689167 9.50284 0.45347518181818175 -0.7031015454545454 9.45406909090909 0.147303975204 0.47495115388899994 90.30396806560002 9.53552427476817 9.4913909847906 6.967318181818177e-2 1.3934545454545422e-2 4.877090909091031e-2 4.687115702479338e-2 4.972128099173549e-2 4.6237355371901406e-2 4.854352264669415e-3 1.9417155702479248e-4 2.378601573553838e-3 3.2568331531720477e-3 3.7676414018760294e-3 2.8993343855747643e-3 5.7068670504682756e-2 6.138111600383321e-2 5.3845467641898744e-2
user_003 Sitting 1.44604752981e12 0.422122 -0.765807 9.54116 0.4325731818181817 -0.710068909090909 9.499356363636364 0.178186982884 0.586460361249 91.0337341456 9.58114719069345 9.536678617258826 1.045118181818172e-2 5.573809090909099e-2 4.180363636363538e-2 8.170777685950412e-2 7.790738016528927e-2 6.587239669421473e-2 1.0922720139669217e-4 3.1067347781900912e-3 1.747544013223058e-3 9.461612793580014e-3 9.708744318026302e-3 7.735971351465028e-3 9.72708219024596e-2 9.853296056663628e-2 8.795437084912283e-2
user_003 Sitting 1.446047529883e12 0.460442 -0.650847 9.46452 0.47786072727272727 -0.6926505454545453 9.454069090909089 0.21200683536400003 0.42360181740899994 89.5771388304 9.49803913885245 9.492320128700781 1.7418727272727252e-2 4.180354545454534e-2 1.0450909090911509e-2 5.130488429752066e-2 9.279201652892563e-2 6.17553719008262e-2 3.034120598016522e-4 1.7475364125702387e-3 1.0922150082649681e-4 3.8283135643719006e-3 1.240843196444929e-2 5.813010988429641e-3 6.1873367165299e-2 0.11139314146054635 7.624310453037468e-2
user_003 Sitting 1.446047529891e12 0.575403 -0.765807 9.50284 0.49876263636363627 -0.678715818181818 9.44710181818182 0.331088612409 0.586460361249 90.30396806560002 9.550995604608874 9.485168028171538 7.664036363636373e-2 8.709118181818198e-2 5.573818181818169e-2 5.130490082644628e-2 8.139087603305785e-2 5.8588429752066e-2 5.873745338314064e-3 7.584873950487632e-3 3.1067449123966797e-3 3.828316097934638e-3 8.9927083140571e-3 5.34964704552959e-3 6.187338763907014e-2 9.482989145863818e-2 7.314128140475522e-2
user_003 Sitting 1.44604753002e12 0.537083 -0.689167 9.50284 0.4778606363636364 -0.6403956363636364 9.502839999999999 0.28845814888899995 0.47495115388899994 90.30396806560002 9.542922894395511 9.537381176494081 5.922236363636357e-2 4.8771363636363585e-2 1.7763568394002505e-15 8.519144628099172e-2 8.424148760330576e-2 4.687074380165254e-2 3.5072883546776786e-3 2.3786459109504084e-3 3.1554436208840472e-30 1.0087168569314048e-2 1.018977686158527e-2 2.9942136691209083e-3 0.10043489716883294 0.10094442461862502 5.471940852312741e-2
user_003 Sitting 1.446047530142e12 0.575403 -0.765807 9.46452 0.3629000909090909 -0.6891668181818181 9.447101818181817 0.331088612409 0.586460361249 89.5771388304 9.512869588302891 9.479941573052752 0.21250290909090908 7.664018181818189e-2 1.7418181818182887e-2 0.10039261983471072 6.618949586776866e-2 7.47398347107437e-2 4.515748637209917e-2 5.873717469123977e-3 3.0339305785127694e-4 1.3279947553097667e-2 6.071256061773864e-3 7.888219504132201e-3 0.11523865476955927 7.791826526414627e-2 8.881564898221597e-2
user_003 Sitting 1.446047530158e12 0.498763 -0.535886 9.50284 0.3698673636363637 -0.6647811818181817 9.461036363636364 0.24876453016900002 0.287173804996 90.30396806560002 9.530997135702277 9.492622848471019 0.12889563636363632 0.12889518181818171 4.180363636363715e-2 9.849253719008265e-2 8.202431404958684e-2 7.125619834710778e-2 1.6614085073586766e-2 1.6613967895942123e-2 1.7475440132232066e-3 1.29092732124846e-2 8.401342212178822e-3 7.35314447483098e-3 0.11361898262387583 9.165883597438286e-2 8.575047798602047e-2
user_003 Sitting 1.446047530198e12 0.422122 -0.535886 9.57948 0.43257318181818183 -0.6403957272727271 9.44361818181818 0.178186982884 0.287173804996 91.7664370704 9.603738743753913 9.47623788966848 1.0451181818181832e-2 0.10450972727272712 0.13586181818181942 9.057513223140498e-2 7.094005785123968e-2 5.7955041322314375e-2 1.0922720139669449e-4 1.0922283094619801e-2 1.8458433639669758e-2 1.2908162652194589e-2 7.0321907231382375e-3 4.926000012021046e-3 0.11361409530597244 8.385815835765914e-2 7.018546866710407e-2
user_003 Sitting 1.446047530247e12 0.307161 -0.880768 9.38788 0.46740963636363625 -0.6264609999999999 9.457552727272729 9.434787992100001e-2 0.775752269824 88.13229089439999 9.43410785629171 9.490591922281 0.16024863636363623 0.25430700000000006 6.967272727272977e-2 7.505712396694214e-2 6.048910743801654e-2 5.067107438016582e-2 2.5679625456404915e-2 6.467205024900004e-2 4.854288925620183e-3 9.283960639918853e-3 9.24644060953268e-3 4.152623526371195e-3 9.635331151506342e-2 9.615841413798731e-2 6.444085293019634e-2
user_003 Sitting 1.446047530328e12 0.345482 -0.574206 9.4262 0.39773645454545453 -0.6473628181818181 9.429683636363636 0.119357812324 0.329712530436 88.85324643999999 9.449990305961165 9.461319720505479 5.225445454545452e-2 7.315681818181807e-2 3.4836363636365775e-3 8.392447107438017e-2 8.550806611570248e-2 5.320462809917343e-2 2.7305280198429726e-3 5.351920046487588e-3 1.2135722314051077e-5 9.723052447205857e-3 1.2296954448760333e-2 5.915613004357611e-3 9.86055396375166e-2 0.1108916338086888 7.691302233274681e-2
user_003 Sitting 1.446047530441e12 0.498763 -0.612526 9.46452 0.5057300909090908 -0.657813909090909 9.429683636363636 0.24876453016900002 0.375188100676 89.5771388304 9.49742551754132 9.466509525966101 6.967090909090812e-3 4.528790909090896e-2 3.4836363636364e-2 6.492278512396693e-2 5.3521900826446235e-2 4.402049586776839e-2 4.8540355735535836e-5 2.0509947098264346e-3 1.213572231404984e-3 5.985194005758828e-3 4.486975113920357e-3 4.422919159729566e-3 7.736403560931157e-2 6.698488720540147e-2 6.650503108584768e-2
user_003 Sitting 1.446047530514e12 0.498763 -0.880768 9.31124 0.4499914545454546 -0.7031015454545453 9.440134545454544 0.24876453016900002 0.775752269824 86.6991903376 9.366093483282825 9.477717120133109 4.877154545454543e-2 0.1776664545454547 0.12889454545454448 6.2389223140495845e-2 6.713966942148762e-2 6.650578512396682e-2 2.378663646024791e-3 3.156536907075212e-2 1.6613803847933633e-2 6.276472416003001e-3 7.296975301380921e-3 6.55549654455295e-3 7.922419085104626e-2 8.542233490944227e-2 8.096602092577447e-2
user_003 Sitting 1.446047530659e12 0.383802 -0.727487 9.54116 0.4465077272727273 -0.6821995454545454 9.461036363636365 0.147303975204 0.529237335169 91.0337341456 9.576548201516713 9.496631596516915 6.270572727272733e-2 4.5287454545454575e-2 8.012363636363418e-2 5.9222214876033095e-2 6.08056611570248e-2 6.428892561983478e-2 3.93200823280166e-3 2.050953539206614e-3 6.419797104131881e-3 4.411940753462063e-3 4.693273525742299e-3 5.314343126070618e-3 6.642244164032261e-2 6.850747058345023e-2 7.289954132963128e-2
user_003 Sitting 1.446047531194e12 0.575403 -0.612526 9.46452 0.4360567272727273 -0.675232090909091 9.485421818181818 0.331088612409 0.375188100676 89.5771388304 9.501758550051933 9.52033802670179 0.13934627272727268 6.270609090909096e-2 2.090181818181769e-2 0.10197616528925618 5.8272214876033075e-2 4.9404297520661444e-2 1.9417383722983458e-2 3.93205383709918e-3 4.368860033057645e-4 1.2546293734994739e-2 5.233893928461308e-3 3.038343568444816e-3 0.11201023942030808 7.23456559059444e-2 5.512117168969484e-2
user_003 Sitting 1.446047531283e12 0.307161 -0.689167 9.50284 0.4325730909090908 -0.6508465454545456 9.44710181818182 9.434787992100001e-2 0.47495115388899994 90.30396806560002 9.532747090918232 9.480348281329318 0.12541209090909078 3.832045454545441e-2 5.573818181818169e-2 8.709162809917352e-2 7.284034710743799e-2 5.162115702479333e-2 1.572819254619005e-2 1.4684572365702374e-3 3.1067449123966797e-3 1.0321058878268211e-2 7.570614707637863e-3 3.4983977688955513e-3 0.1015926123213111 8.700927943408027e-2 5.9147254956553576e-2
user_003 Sitting 1.446047531348e12 0.613724 -0.765807 9.57948 0.46044236363636365 -0.7379379999999999 9.443618181818183 0.37665714817600005 0.586460361249 91.7664370704 9.629618610299424 9.484515872090418 0.1532816363636364 2.7869000000000144e-2 0.13586181818181764 8.424131404958675e-2 6.713955371900827e-2 6.777256198347087e-2 2.349526004631406e-2 7.76681161000008e-4 1.8458433639669276e-2 1.073036766763711e-2 7.2020997030293e-3 5.847211660405668e-3 0.10358748798786999 8.48651854592288e-2 7.646706258517891e-2
user_003 Sitting 1.446047531509e12 0.383802 -0.650847 9.46452 0.4499912727272728 -0.6543302727272727 9.440134545454542 0.147303975204 0.42360181740899994 89.5771388304 9.494632411158054 9.473935581651636 6.618927272727282e-2 3.4832727272727793e-3 2.438545454545782e-2 4.940451239669421e-2 4.307072727272726e-2 5.193785123966954e-2 4.381019824165301e-3 1.2133188892562345e-5 5.946503933885893e-4 4.212253419712996e-3 3.38923822532682e-3 4.649084893764115e-3 6.490187531738198e-2 5.821716435319415e-2 6.818419827030392e-2
user_003 Sitting 1.446047531598e12 0.498763 -0.689167 9.46452 0.4813443636363637 -0.6856832727272727 9.468003636363637 0.24876453016900002 0.47495115388899994 89.5771388304 9.502676176449349 9.506151313791571 1.741863636363633e-2 3.4837272727272772e-3 3.4836363636365775e-3 8.740837190082638e-2 5.605531404958677e-2 7.062280991735535e-2 3.034088927685939e-4 1.2136355710743833e-5 1.2135722314051077e-5 1.465137964412546e-2 5.0474440098054055e-3 7.304601585574778e-3 0.12104288349227914 7.104536585735487e-2 8.54669619535805e-2
user_003 Sitting 1.44604753193e12 0.460442 -0.880768 9.46452 0.4534750909090908 -0.7170360909090907 9.422716363636363 0.21200683536400003 0.775752269824 89.5771388304 9.516559143702517 9.461390118682749 6.96690909090919e-3 0.1637319090909093 4.180363636363715e-2 3.0719553719008252e-2 7.727383471074388e-2 5.320462809917359e-2 4.853782228099312e-5 2.6808138054553784e-2 1.7475440132232066e-3 1.446381519275732e-3 9.485840937113464e-3 5.361782767843718e-3 3.8031322870441045e-2 9.7395281903763e-2 7.322419523520704e-2
user_003 Sitting 1.446047531955e12 0.422122 -0.650847 9.65612 0.47786072727272727 -0.6996178181818181 9.44710181818182 0.178186982884 0.42360181740899994 93.24065345439999 9.687230886826894 9.485730492495545 5.573872727272727e-2 4.8770818181818165e-2 0.20901818181818044 4.402082644628096e-2 8.455785123966947e-2 6.808925619834692e-2 3.106805717983471e-3 2.3785927061239654e-3 4.3688600330577934e-2 4.2089599727242605e-3 1.0109191196815939e-2 7.540696546957087e-3 6.487649784570881e-2 0.10054447372588877 8.68371841261397e-2
user_003 Sitting 1.446047532084e12 0.383802 -0.650847 9.46452 0.47786072727272716 -0.6612976363636363 9.450585454545456 0.147303975204 0.42360181740899994 89.5771388304 9.494632411158054 9.486668111432918 9.405872727272718e-2 1.0450636363636301e-2 1.3934545454544534e-2 6.555622314049582e-2 7.949095041322311e-2 7.03061157024793e-2 8.847044176165272e-3 1.0921580040495736e-4 1.941715570247677e-4 5.857225243961679e-3 1.1110982175987227e-2 7.402790611570207e-3 7.65325110261102e-2 0.10540864374417891 8.603947124180975e-2
user_003 Sitting 1.446047532165e12 0.422122 -0.574206 9.54116 0.44650772727272725 -0.6369118181818182 9.433167272727273 0.178186982884 0.329712530436 91.0337341456 9.567739213571825 9.465520089793488 2.4385727272727253e-2 6.27058181818182e-2 0.1079927272727268 5.953895867768593e-2 3.927050413223136e-2 6.808925619834726e-2 5.946636946198338e-4 3.932019633851242e-3 1.166242914380155e-2 4.64693759204658e-3 2.0719397710060082e-3 7.326666535236722e-3 6.816845012208052e-2 4.551856512463907e-2 8.559594929222247e-2
user_003 Sitting 1.446047532214e12 0.537083 -0.612526 9.54116 0.463926 -0.6299445454545455 9.443618181818179 0.28845814888899995 0.375188100676 91.0337341456 9.575874915388411 9.47633465958667 7.315699999999997e-2 1.7418545454545464e-2 9.754181818182062e-2 4.655442975206612e-2 4.655447107438018e-2 4.9087603305785876e-2 5.351946648999996e-3 3.0340572575206643e-4 9.514406294215351e-3 3.2932427384973705e-3 2.640112742971452e-3 3.719047265514745e-3 5.7386781914456314e-2 5.1382027431500325e-2 6.09839918791378e-2
user_003 Sitting 1.446047532391e12 0.460442 -0.535886 9.4262 0.41863836363636364 -0.6299446363636363 9.461036363636364 0.21200683536400003 0.287173804996 88.85324643999999 9.452641275345213 9.492556516525278 4.1803636363636376e-2 9.405863636363632e-2 3.4836363636364e-2 9.659232231404959e-2 8.835825619834711e-2 6.49223140495872e-2 1.7475440132231415e-3 8.847027074586768e-3 1.213572231404984e-3 1.4473703594323817e-2 1.2876186440492116e-2 5.98070460586029e-3 0.12030670635639484 0.11347328514012502 7.733501539315997e-2
user_003 Sitting 1.446047532529e12 0.498763 -0.689167 9.34956 0.42560581818181814 -0.6752322727272727 9.481938181818181 0.24876453016900002 0.47495115388899994 87.41427219360001 9.388183417342145 9.515991487267254 7.315718181818187e-2 1.3934727272727265e-2 0.13237818181818106 7.98074214876033e-2 4.908786776859502e-2 6.808925619834709e-2 5.3519732515785205e-3 1.9417662416528904e-4 1.7523983021487402e-2 7.866250311642372e-3 3.222624247057847e-3 6.397732154470296e-3 8.869188413627467e-2 5.676816226599067e-2 7.998582470957148e-2
user_003 Sitting 1.446047532691e12 0.422122 -0.842448 9.46452 0.42908936363636363 -0.6787158181818183 9.405298181818182 0.178186982884 0.7097186327039999 89.5771388304 9.511311394649425 9.440375723637255 6.967363636363633e-3 0.16373218181818172 5.9221818181818264e-2 4.497070247933884e-2 8.96250743801653e-2 6.048859504132167e-2 4.854415604132226e-5 2.6808227362942118e-2 3.5072237487603405e-3 3.0802885080879025e-3 1.2626851415314798e-2 4.959097436513814e-3 5.550034691862658e-2 0.11236926365921776 7.042085938494229e-2
user_003 Sitting 1.446047532788e12 0.460442 -0.689167 9.54116 0.4360566363636364 -0.6403957272727273 9.436650909090908 0.21200683536400003 0.47495115388899994 91.0337341456 9.57709205003549 9.468743163819505 2.438536363636362e-2 4.877127272727266e-2 0.104509090909092 4.117052066115701e-2 5.162148760330579e-2 5.35213223140498e-2 5.946459596776853e-4 2.3786370434380104e-3 1.0922150082644855e-2 2.744925226993988e-3 4.317064291385426e-3 4.449397099323852e-3 5.239203400321454e-2 6.570437041312721e-2 6.670380123594045e-2
user_003 Sitting 1.446047532804e12 0.230521 -0.574206 9.54116 0.41167100000000006 -0.636912 9.454069090909092 5.3139931441e-2 0.329712530436 91.0337341456 9.561202152840247 9.484988102207778 0.18115000000000006 6.270600000000004e-2 8.709090909090733e-2 5.225482644628099e-2 6.0805702479338856e-2 6.017190082644642e-2 3.281532250000002e-2 3.932042436000005e-3 7.584826446280685e-3 5.409289030824944e-3 5.143409093702481e-3 5.145546261157036e-3 7.354786897541589e-2 7.171756475022337e-2 7.173246309138587e-2
user_003 Sitting 1.446047532819e12 0.575403 -0.727487 9.34956 0.42212199999999994 -0.6403956363636364 9.450585454545454 0.331088612409 0.529237335169 87.41427219360001 9.395456249761265 9.482358118978716 0.15328100000000006 8.70913636363636e-2 0.10102545454545364 6.55560991735537e-2 7.157335537190083e-2 6.935603305785162e-2 2.349506496100002e-2 7.584905620041317e-3 1.0206142466115519e-2 7.620226583552217e-3 6.374646010217882e-3 6.172669667918895e-3 8.729390920076965e-2 7.984138031257904e-2 7.856633928037436e-2
user_003 Sitting 1.446047532991e12 0.498763 -0.689167 9.46452 0.41863836363636364 -0.6578139090909092 9.408781818181819 0.24876453016900002 0.47495115388899994 89.5771388304 9.502676176449349 9.441844129998412 8.012463636363637e-2 3.1353090909090775e-2 5.573818181818169e-2 7.474038842975207e-2 6.58730082644628e-2 6.080528925619788e-2 6.41995735240496e-3 9.830163095537105e-4 3.1067449123966797e-3 6.935123140278735e-3 7.1513644837716e-3 6.11640404628094e-3 8.327738672820333e-2 8.456574060322301e-2 7.820744239700554e-2
user_003 Sitting 1.446047533055e12 0.460442 -0.650847 9.38788 0.42212200000000005 -0.6578139090909091 9.415749090909088 0.21200683536400003 0.42360181740899994 88.13229089439999 9.421671802136444 9.44895072125354 3.8319999999999965e-2 6.966909090909135e-3 2.7869090909089067e-2 7.695723966942146e-2 6.523954545454545e-2 5.225454545454495e-2 1.4684223999999974e-3 4.8537822280992347e-5 7.766862280990708e-4 7.050963895679938e-3 7.138123901706236e-3 4.8355337184071805e-3 8.397001783779695e-2 8.448741860008646e-2 6.953800197307354e-2
user_003 Sitting 1.446047533249e12 0.345482 -0.650847 9.46452 0.4256057272727272 -0.6578139090909091 9.436650909090908 0.119357812324 0.42360181740899994 89.5771388304 9.493160614891808 9.46968381931937 8.012372727272721e-2 6.966909090909135e-3 2.786909090909262e-2 5.85887603305785e-2 5.953899173553718e-2 4.4337190082644765e-2 6.419811672074369e-3 4.8537822280992347e-5 7.766862280992689e-4 4.047867299084896e-3 6.319509547628849e-3 3.5458374106687065e-3 6.362285201941906e-2 7.949534293044372e-2 5.954693451949233e-2
user_003 Sitting 1.446047533443e12 0.498763 -0.650847 9.4262 0.4499913636363637 -0.657814 9.4262 0.24876453016900002 0.42360181740899994 88.85324643999999 9.461797545264748 9.460293159957134 4.8771636363636295e-2 6.9670000000000565e-3 0.0 5.193814049586775e-2 5.257162809917355e-2 2.660231404958728e-2 2.37867251358677e-3 4.853908900000079e-5 0.0 3.3914277338775323e-3 5.8075949420383155e-3 9.09075926070645e-4 5.823596598217919e-2 7.620757798302158e-2 3.0150885991470384e-2
user_003 Sitting 1.446047533702e12 0.422122 -0.650847 9.50284 0.4395403636363637 -0.6612977272727272 9.443618181818183 0.178186982884 0.42360181740899994 90.30396806560002 9.534451052152557 9.477111134477436 1.7418363636363676e-2 1.0450727272727223e-2 5.9221818181818264e-2 3.4203123966942146e-2 2.786920661157025e-2 2.72357024793389e-2 3.0339939176859645e-4 1.0921770052892458e-4 3.5072237487603405e-3 1.6593011434440253e-3 1.3106807544943642e-3 1.1385514025544887e-3 4.073452029230276e-2 3.62033251856009e-2 3.374242733643341e-2
user_003 Sitting 1.44604753435e12 0.498763 -0.689167 9.50284 0.45695872727272735 -0.6612978181818181 9.468003636363635 0.24876453016900002 0.47495115388899994 90.30396806560002 9.540842926579288 9.502149947082033 4.180427272727266e-2 2.7869181818181876e-2 3.4836363636365775e-2 2.945285950413223e-2 1.8051628099173548e-2 3.293619834710784e-2 1.7475972182561929e-3 7.766912952148793e-4 1.2135722314051078e-3 1.126443607117956e-3 5.284638936957168e-4 1.4783516273478882e-3 3.356253278758854e-2 2.2988342560865863e-2 3.844933845136855e-2
user_003 Sitting 1.446047534415e12 0.498763 -0.650847 9.46452 0.4639260909090909 -0.6612978181818181 9.46452 0.24876453016900002 0.42360181740899994 89.5771388304 9.499973956699987 9.499015665677254 3.4836909090909085e-2 1.0450818181818144e-2 0.0 3.103636363636363e-2 1.805163636363636e-2 2.7552396694215275e-2 1.213610235008264e-3 1.0921960066942071e-4 0.0 1.2091900474124713e-3 5.284640664357619e-4 1.1595131047333121e-3 3.477341006304201e-2 2.2988346317988205e-2 3.405162411300395e-2
user_003 Sitting 1.446047534803e12 0.422122 -0.612526 9.46452 0.4604424545454545 -0.6543305454545453 9.471487272727273 0.178186982884 0.375188100676 89.5771388304 9.493709175762653 9.505321529005101 3.832045454545452e-2 4.180454545454526e-2 6.967272727273155e-3 3.4520173553719e-2 1.3301223140495816e-2 2.026842975206639e-2 1.4684572365702459e-3 1.7476200206611408e-3 4.854288925620431e-5 1.6096746418955666e-3 3.4863351750112544e-4 9.443798455296936e-4 4.012075076435592e-2 1.8671730436709003e-2 3.0730763829259006e-2
user_003 Sitting 1.446047534998e12 0.460442 -0.689167 9.4262 0.453475 -0.6543305454545454 9.461036363636362 0.21200683536400003 0.47495115388899994 88.85324643999999 9.462568595748884 9.494558667728176 6.967000000000001e-3 3.483645454545459e-2 3.483636363636222e-2 2.8502826446280997e-2 1.3934595041322238e-2 1.8051570247933538e-2 4.8539089000000014e-5 1.2135785652975235e-3 1.2135722314048601e-3 1.319511052964688e-3 3.7069852473929204e-4 5.924438984222251e-4 3.632507471382114e-2 1.9253532785940664e-2 2.434017046822444e-2
user_003 Sitting 1.446047535515e12 0.460442 -0.650847 9.46452 0.44650754545454546 -0.6647814545454546 9.440134545454544 0.21200683536400003 0.42360181740899994 89.5771388304 9.49803913885245 9.474119764777338 1.3934454545454555e-2 1.3934454545454611e-2 2.4385454545456042e-2 2.4068826446280996e-2 2.0585239669421454e-2 3.008595041322305e-2 1.941690234793391e-4 1.9416902347934065e-4 5.946503933885027e-4 8.980566373538687e-4 6.454093360931615e-4 1.2367404285499523e-3 2.9967593119132354e-2 2.5404907716682648e-2 3.516732046303716e-2
user_003 Sitting 1.446047537963e12 2.91294 -4.06135 -17.7429 0.6694618181818182 -0.9748269999999999 7.00156909090909 8.485219443599998 16.4945638225 314.81050041 18.433401305133568 10.321177531628067 2.2434781818181815 3.086523 24.74446909090909 0.2169370991735537 0.3173297520661157 2.264065123966943 5.033194352294213 9.526624229529 612.2887505909553 0.457926093891347 0.8678727182561082 55.66323812816227 0.6767023672866432 0.9315968646663149 7.4607799946226985
user_003 Sitting 1.446047537996e12 0.498763 -0.574206 9.38788 0.7008150000000001 -0.9574087272727273 7.0050527272727265 0.24876453016900002 0.329712530436 88.13229089439999 9.418639389795374 10.325252885713102 0.20205200000000006 0.3832027272727273 2.3828272727272726 0.2704586033057851 0.4246898595041323 3.15778347107438 4.082501070400003e-2 0.14684433018925622 5.677865811652892 0.467783707752465 0.9122205865213097 57.8899981788081 0.6839471527482697 0.9551023958305778 7.608547704970253
user_003 Sitting 1.446047538044e12 0.422122 -0.919089 9.50284 0.6903640909090908 -0.9643761818181816 7.005052727272727 0.178186982884 0.8447245899210001 90.30396806560002 9.556509804233187 10.325897387815681 0.2682420909090908 4.528718181818159e-2 2.4977872727272734 0.41043860330578513 0.5539019090909091 4.500261157024793 7.195381933528093e-2 2.050928837033037e-3 6.2389412597983505 0.5123842726084574 0.959901352937687 61.24369845327421 0.7158102210840925 0.9797455552018018 7.825835319841213
user_003 Sitting 1.446047538101e12 0.383802 -0.804128 9.54116 0.443024 -0.7135526363636363 9.461036363636364 0.147303975204 0.646621840384 91.0337341456 9.582674989854764 9.498997704798395 5.9222e-2 9.057536363636365e-2 8.012363636363595e-2 0.13871318181818182 0.11464396694214875 0.9611742148760336 3.5072452839999997e-3 8.203896497859506e-3 6.419797104132165e-3 3.661955596183396e-2 2.796989594571301e-2 2.23701703117055 0.1913623681966597 0.1672420280483139 1.4956660827773525
user_003 Sitting 1.446047538125e12 0.498763 -0.804128 9.57948 0.47089336363636375 -0.7240035454545454 9.450585454545454 0.24876453016900002 0.646621840384 91.7664370704 9.626101154722663 9.490513908927614 2.7869636363636263e-2 8.012445454545458e-2 0.12889454545454626 6.175596694214875e-2 5.922220661157021e-2 0.3128957024793395 7.767166310413167e-4 6.419928216206618e-3 1.661380384793409e-2 8.979472165661901e-3 4.764998892272725e-3 0.5763698394401208 9.476007685550862e-2 6.902897139804942e-2 0.7591902524664821
user_003 Sitting 1.446047538262e12 0.537083 -0.612526 9.50284 0.5092136363636363 -0.6543302727272726 9.485421818181818 0.28845814888899995 0.375188100676 90.30396806560002 9.537694391998782 9.522259443822756 2.786936363636372e-2 4.180427272727261e-2 1.7418181818182887e-2 7.220681818181819e-2 6.175582644628099e-2 6.1121983471074254e-2 7.767014294958724e-4 1.7475972182561883e-3 3.0339305785127694e-4 9.30272696033734e-3 5.69174341896544e-3 5.808597998497331e-3 9.645064520436004e-2 7.544364399315187e-2 7.621415877970006e-2
user_003 Sitting 1.446047538343e12 0.537083 -0.574206 9.38788 0.4743770909090909 -0.7065851818181819 9.471487272727272 0.28845814888899995 0.329712530436 88.13229089439999 9.420746338466236 9.51013996484748 6.270590909090906e-2 0.13237918181818187 8.360727272727253e-2 4.782130578512396e-2 6.175572727272729e-2 5.5104793388430065e-2 3.932031034917352e-3 1.7524247778851254e-2 6.990176052892529e-3 3.4631438297821194e-3 5.9587168723117985e-3 3.907702585123994e-3 5.88484819666754e-2 7.719272551420761e-2 6.251161960087095e-2
user_003 Sitting 1.446047538481e12 0.422122 -0.650847 9.50284 0.42908945454545455 -0.7031014545454545 9.415749090909092 0.178186982884 0.42360181740899994 90.30396806560002 9.534451052152557 9.452520129048189 6.9674545454545544e-3 5.225445454545452e-2 8.709090909090911e-2 5.162155371900827e-2 7.600711570247934e-2 8.075702479338903e-2 4.854542284297533e-5 2.7305280198429726e-3 7.584826446280995e-3 5.528469067821186e-3 9.055587604848238e-3 7.911387701277323e-3 7.435367555017833e-2 9.516085121964935e-2 8.894598192879385e-2
user_003 Sitting 1.446047538554e12 0.422122 -0.535886 9.4262 0.4465077272727273 -0.6647812727272726 9.422716363636363 0.178186982884 0.287173804996 88.85324643999999 9.450852195854086 9.457397142342744 2.438572727272731e-2 0.12889527272727264 3.4836363636365775e-3 4.940454545454545e-2 7.474023140495865e-2 5.637157024793347e-2 5.946636946198365e-4 1.6613991331437993e-2 1.2135722314051077e-5 4.071027434838466e-3 8.259009006755818e-3 4.830017480991683e-3 6.380460355521744e-2 9.087909004141612e-2 6.94983271812472e-2
user_003 Sitting 1.446047538586e12 0.345482 -0.689167 9.4262 0.4465078181818182 -0.6299447272727272 9.398330909090907 0.119357812324 0.47495115388899994 88.85324643999999 9.457671775136468 9.430760240156756 0.10102581818181816 5.922227272727276e-2 2.786909090909262e-2 5.3204925619834725e-2 9.469222314049584e-2 4.5603966942148494e-2 1.020621593930578e-2 3.5072775869834753e-3 7.766862280992689e-4 4.033517999304282e-3 1.2079629896032291e-2 3.5149464811419576e-3 6.350998346169114e-2 0.10990736961656526 5.928698407864881e-2
user_003 Sitting 1.446047538716e12 0.422122 -0.650847 9.4262 0.46044236363636365 -0.6508465454545453 9.457552727272729 0.178186982884 0.42360181740899994 88.85324643999999 9.458067204259704 9.49159945306404 3.832036363636365e-2 4.5454545460899e-7 3.13527272727292e-2 5.098814049586778e-2 5.57385867768595e-2 6.143867768595047e-2 1.4684502692231417e-3 2.0661157030569337e-13 9.829935074381372e-4 4.204520725820437e-3 5.136800779629599e-3 5.889135064763309e-3 6.484227576065199e-2 7.167147814597938e-2 7.674070018421325e-2
user_003 Sitting 1.446047538942e12 0.307161 -0.574206 9.57948 0.41863845454545456 -0.6334282727272728 9.478454545454547 9.434787992100001e-2 0.329712530436 91.7664370704 9.601588279069095 9.509319384860925 0.11147745454545455 5.922227272727276e-2 0.10102545454545364 5.573864462809917e-2 5.478864462809916e-2 4.40204958677692e-2 1.2427222871933884e-2 3.5072775869834753e-3 1.0206142466115519e-2 4.095318860127722e-3 5.583616413305784e-3 2.7879063897821754e-3 6.39946783735001e-2 7.472360010937498e-2 5.280062868737621e-2
user_003 Sitting 1.446047539177e12 0.345482 -0.689167 9.46452 0.3907692727272727 -0.6821995454545454 9.468003636363637 0.119357812324 0.47495115388899994 89.5771388304 9.495864773500779 9.501078447172395 4.5287272727272676e-2 6.9674545454545544e-3 3.4836363636365775e-3 6.84062644628099e-2 5.985547107438018e-2 6.302214876033106e-2 2.0509370710743756e-3 4.854542284297533e-5 1.2135722314051077e-5 7.985403573391432e-3 5.155520228918111e-3 8.248981431104595e-3 8.936108534139137e-2 7.180195142834289e-2 9.082390341261817e-2
user_003 Sitting 1.446047539242e12 0.307161 -0.574206 9.46452 0.42560581818181814 -0.6403957272727273 9.471487272727272 9.434787992100001e-2 0.329712530436 89.5771388304 9.48689618583217 9.503357170811485 0.11844481818181812 6.618972727272732e-2 6.967272727271379e-3 6.492270247933883e-2 6.048900000000001e-2 7.347305785123949e-2 1.4029174954123954e-2 4.381079996438023e-3 4.8542889256179554e-5 7.264995577235909e-3 6.130837874947407e-3 9.196671019083402e-3 8.52349434048965e-2 7.829966714455054e-2 9.589927538351581e-2
user_003 Sitting 1.44604753925e12 0.575403 -0.650847 9.54116 0.4290894545454545 -0.6473630909090909 9.46452 0.331088612409 0.42360181740899994 91.0337341456 9.580627566888193 9.497061195942141 0.1463135454545455 3.48390909090901e-3 7.663999999999938e-2 6.618947107438017e-2 5.1938214876033055e-2 6.428892561983429e-2 2.1407653583479354e-2 1.2137622553718444e-5 5.8736895999999044e-3 7.6180346566506385e-3 5.266982370293012e-3 6.86109609737033e-3 8.728135343044721e-2 7.257397860316749e-2 8.283173363735864e-2
user_003 Sitting 1.446047539363e12 0.460442 -0.727487 9.34956 0.4569588181818181 -0.6717486363636362 9.4262 0.21200683536400003 0.529237335169 87.41427219360001 9.389116910771374 9.462187082718389 3.483181818181913e-3 5.573836363636375e-2 7.663999999999938e-2 8.455800826446282e-2 7.157352066115702e-2 6.365553719008284e-2 1.2132555578513057e-5 3.106765180859517e-3 5.8736895999999044e-3 9.295014362248687e-3 9.007034869194588e-3 5.014259810668705e-3 9.641065481703091e-2 9.49053995787099e-2 7.081143841688788e-2
user_003 Sitting 1.446047539436e12 0.460442 -0.765807 9.54116 0.42560581818181814 -0.7135525454545454 9.447101818181817 0.21200683536400003 0.586460361249 91.0337341456 9.582911944822044 9.484323546353263 3.483618181818188e-2 5.225445454545463e-2 9.405818181818226e-2 7.030644628099174e-2 6.903965289256202e-2 6.903933884297525e-2 1.2135595636694255e-3 2.7305280198429843e-3 8.846941566942232e-3 6.440833891956421e-3 8.33402396231856e-3 8.223606738993262e-3 8.025480603650115e-2 9.129087556989778e-2 9.068410411419006e-2
user_003 Sitting 1.446047539468e12 0.460442 -0.765807 9.34956 0.44999136363636355 -0.7170361818181819 9.4262 0.21200683536400003 0.586460361249 87.41427219360001 9.392163722498294 9.46466076088866 1.0450636363636467e-2 4.8770818181818165e-2 7.663999999999938e-2 6.840630578512398e-2 3.7686694214876054e-2 7.727338842975164e-2 1.0921580040496085e-4 2.3785927061239654e-3 5.8736895999999044e-3 6.29520499386251e-3 2.36428181288505e-3 9.046629361382369e-3 7.934232788280483e-2 4.862388109648437e-2 9.511377061909788e-2
user_003 Sitting 1.446047539525e12 0.460442 -0.727487 9.38788 0.4290893636363636 -0.6821993636363636 9.429683636363636 0.21200683536400003 0.529237335169 88.13229089439999 9.427276121178004 9.464803624816936 3.1352636363636444e-2 4.528763636363642e-2 4.180363636363715e-2 6.397267768595044e-2 5.510515702479342e-2 6.650578512396699e-2 9.829878069504182e-4 2.050970007404964e-3 1.7475440132232066e-3 8.124416326288506e-3 5.511913618561984e-3 5.330891838317037e-3 9.013554418922928e-2 7.424226302155655e-2 7.301295664686534e-2
user_003 Sitting 1.446047539541e12 0.345482 -0.727487 9.4262 0.41515472727272723 -0.6891666363636363 9.4262 0.119357812324 0.529237335169 88.85324643999999 9.460541294634941 9.461245060511372 6.967272727272722e-2 3.832036363636371e-2 0.0 6.618949586776862e-2 6.143910743801655e-2 6.682247933884321e-2 4.854288925619827e-3 1.468450269223146e-3 0.0 8.582264722732536e-3 5.798763261621339e-3 6.938323421187104e-3 9.264051339847236e-2 7.614961104051247e-2 8.329659909736474e-2
user_003 Sitting 1.446047539613e12 0.460442 -0.574206 9.38788 0.4012200909090909 -0.6856830909090909 9.44361818181818 0.21200683536400003 0.329712530436 88.13229089439999 9.41668786039975 9.477938578653424 5.922190909090913e-2 0.11147709090909086 5.573818181818169e-2 6.4289347107438e-2 8.930847107438017e-2 6.143867768595079e-2 3.5072345163719054e-3 1.2427141797553708e-2 3.1067449123966797e-3 5.837369956217128e-3 1.0567076387593537e-2 6.332640552967716e-3 7.640268291242873e-2 0.10279628586477985 7.957788984993078e-2
user_003 Sitting 1.446047539662e12 0.460442 -0.574206 9.50284 0.42212209090909086 -0.664781090909091 9.468003636363637 0.21200683536400003 0.329712530436 90.30396806560002 9.531300406104092 9.501586987084501 3.8319909090909154e-2 9.0575090909091e-2 3.4836363636364e-2 6.618954545454546e-2 8.550803305785125e-2 3.9586776859504624e-2 1.468415432735542e-3 8.203847093190098e-3 1.213572231404984e-3 8.463145261121711e-3 8.296535774210368e-3 2.9379480474831074e-3 9.199535456272621e-2 9.108532139818341e-2 5.4202841691954745e-2
user_003 Sitting 1.446047539743e12 0.307161 -0.650847 9.38788 0.443024 -0.6647812727272728 9.447101818181817 9.434787992100001e-2 0.42360181740899994 88.13229089439999 9.415425672359694 9.48130930593024 0.13586299999999996 1.3934272727272878e-2 5.9221818181818264e-2 6.36560826446281e-2 4.053709090909094e-2 4.718743801652924e-2 1.845875476899999e-2 1.9416395643802073e-4 3.5072237487603405e-3 5.967562775254698e-3 2.700786287416983e-3 2.8695467035311996e-3 7.725000178158378e-2 5.196908973050214e-2 5.3568150085019736e-2
user_003 Sitting 1.44604753984e12 0.345482 -0.650847 9.57948 0.4465079090909091 -0.6647812727272727 9.44710181818182 0.119357812324 0.42360181740899994 91.7664370704 9.607777927290629 9.481999925423107 0.10102590909090908 1.3934272727272767e-2 0.13237818181818106 8.139092561983471e-2 7.917409917355371e-2 6.04885950413228e-2 1.0206234307644627e-2 1.9416395643801764e-4 1.7523983021487402e-2 7.2760015071224645e-3 1.0569256395184072e-2 5.581329016979755e-3 8.529948128284523e-2 0.10280688885081618 7.47082928260294e-2
user_003 Sitting 1.446047539938e12 0.537083 -0.574206 9.4262 0.4499914545454545 -0.6787157272727273 9.457552727272727 0.28845814888899995 0.329712530436 88.85324643999999 9.458933191397696 9.493288075858345 8.70915454545455e-2 0.10450972727272734 3.135272727272742e-2 5.7638661157024804e-2 7.410695041322317e-2 3.895338842975268e-2 7.584937289661166e-3 1.0922283094619848e-2 9.829935074380258e-4 4.463789009020284e-3 8.106787283856505e-3 2.737157005559762e-3 6.68115933728592e-2 9.003769923680027e-2 5.2317845956802944e-2
user_003 Sitting 1.446047540156e12 0.345482 -0.804128 9.46452 0.453475 -0.6926506363636363 9.443618181818183 0.119357812324 0.646621840384 89.5771388304 9.504899709260902 9.480333405363366 0.107993 0.11147736363636362 2.090181818181769e-2 4.718766942148758e-2 5.4788471074380146e-2 6.333884297520678e-2 1.1662488049e-2 1.2427202603314046e-2 4.368860033057645e-4 5.102591182545451e-3 4.019181194645379e-3 5.653040103380977e-3 7.143242388821376e-2 6.339701250568026e-2 7.518670163919267e-2
user_003 Sitting 1.446047540172e12 0.498763 -0.765807 9.4262 0.45347509090909094 -0.6926505454545454 9.45406909090909 0.24876453016900002 0.586460361249 88.85324643999999 9.470399745069793 9.490850263665708 4.528790909090907e-2 7.315645454545461e-2 2.7869090909090843e-2 5.2888297520661126e-2 6.555606611570247e-2 6.3655537190083e-2 2.0509947098264446e-3 5.351866841661166e-3 7.766862280991699e-4 5.354138748736284e-3 5.332058540061606e-3 5.5967744817431225e-3 7.31719806260312e-2 7.30209458995267e-2 7.481159323088316e-2
user_003 Sitting 1.446047540269e12 0.460442 -0.650847 9.2346 0.45695872727272724 -0.6682647272727272 9.394847272727274 0.21200683536400003 0.42360181740899994 85.27783716 9.26895063169359 9.43032809691739 3.4832727272727793e-3 1.741772727272728e-2 0.16024727272727368 5.383861983471073e-2 7.347342975206611e-2 8.645752066115685e-2 1.2133188892562345e-5 3.0337722334710765e-4 2.567918841652923e-2 5.776714665064613e-3 7.215338384983472e-3 1.0210555456048083e-2 7.600470159841832e-2 8.494314795781631e-2 0.10104729316536927
user_003 Sitting 1.446047540318e12 0.422122 -0.535886 9.65612 0.45695872727272724 -0.668264909090909 9.440134545454546 0.178186982884 0.287173804996 93.24065345439999 9.680186684268026 9.475438618282498 3.483672727272724e-2 0.132378909090909 0.2159854545454536 6.428949586776858e-2 5.7955223140495844e-2 8.962446280991737e-2 1.213597567074378e-3 1.752417557209915e-2 4.66497165752062e-2 6.929614733910591e-3 4.520045244982718e-3 1.2364094543050317e-2 8.324430751655389e-2 6.723128174430945e-2 0.11119395011892651
user_003 Sitting 1.446047540325e12 0.383802 -0.574206 9.46452 0.4360567272727273 -0.6508466363636364 9.44361818181818 0.147303975204 0.329712530436 89.5771388304 9.489686788089479 9.476578365490541 5.225472727272734e-2 7.664063636363638e-2 2.0901818181819465e-2 5.6688727272727266e-2 5.763855371900824e-2 8.930776859504132e-2 2.7305565223471146e-3 5.873787142223143e-3 4.368860033058388e-4 5.49977403832757e-3 4.470402678275729e-3 1.2349752325770074e-2 7.41604614220244e-2 6.686106997555251e-2 0.11112943950983499
user_003 Sitting 1.44604754035e12 0.345482 -0.804128 9.34956 0.44650772727272714 -0.6647813636363636 9.408781818181819 0.119357812324 0.646621840384 87.41427219360001 9.390434060591023 9.44335301311665 0.10102572727272713 0.1393466363636363 5.9221818181818264e-2 5.478842148760328e-2 6.143899999999997e-2 8.645752066115717e-2 1.0206197570983441e-2 1.941748506585949e-2 3.5072237487603405e-3 4.3148482379737e-3 5.454524538504126e-3 1.1695526568294479e-2 6.568750442796331e-2 7.38547529851947e-2 0.10814585784159501
user_003 Sitting 1.446047540366e12 0.460442 -0.727487 9.38788 0.44999136363636355 -0.668265 9.412265454545453 0.21200683536400003 0.529237335169 88.13229089439999 9.427276121178004 9.447275769909304 1.0450636363636467e-2 5.9222e-2 2.4385454545454266e-2 6.017223966942149e-2 6.365590909090904e-2 6.238876033057863e-2 1.0921580040496085e-4 3.5072452839999997e-3 5.946503933884161e-4 5.200762819015026e-3 5.541682701910585e-3 7.90476821637862e-3 7.21163145135345e-2 7.444247914941163e-2 8.890876343971171e-2
user_003 Sitting 1.44604754048e12 0.498763 -0.765807 9.4262 0.4987627272727273 -0.7414219090909092 9.44361818181818 0.24876453016900002 0.586460361249 88.85324643999999 9.470399745069793 9.486452058500035 2.7272727270988284e-7 2.43850909090908e-2 1.741818181818111e-2 6.397279338842976e-2 7.505698347107435e-2 5.6371570247933954e-2 7.43801652797708e-14 5.946326586446228e-4 3.0339305785121503e-4 5.997347520679191e-3 8.279990516842221e-3 4.944755219233634e-3 7.744254335104957e-2 9.099445322019481e-2 7.031895348505718e-2
user_003 Sitting 1.446047540593e12 0.460442 -0.689167 9.50284 0.42560572727272733 -0.668265 9.502839999999999 0.21200683536400003 0.47495115388899994 90.30396806560002 9.538916398357468 9.536132101776438 3.483627272727269e-2 2.0901999999999976e-2 1.7763568394002505e-15 5.858879338842975e-2 4.3703983471074376e-2 9.310809917355378e-2 1.213565897528923e-3 4.36893603999999e-4 3.1554436208840472e-30 4.6480467704342575e-3 2.341116897894815e-3 1.3706746729977431e-2 6.817658520661077e-2 4.838508962371378e-2 0.11707581616191036
user_003 Sitting 1.446047540649e12 0.652044 -0.574206 9.50284 0.4465077272727273 -0.6299446363636364 9.443618181818183 0.42516137793599995 0.329712530436 90.30396806560002 9.542475673218771 9.476115480764772 0.20553627272727265 5.573863636363641e-2 5.9221818181818264e-2 8.360787603305782e-2 6.93565371900826e-2 7.442314049586765e-2 4.2245159406619805e-2 3.1067955836776907e-3 3.5072237487603405e-3 1.1187097730272723e-2 6.7685262636356025e-3 8.376958139143426e-3 0.10576907738215703 8.227105361933565e-2 9.152572392034616e-2
user_003 Sitting 1.44604754073e12 0.422122 -0.765807 9.38788 0.47437709090909086 -0.6856831818181817 9.450585454545454 0.178186982884 0.586460361249 88.13229089439999 9.428517287385805 9.487907311509131 5.225509090909086e-2 8.012381818181835e-2 6.270545454545484e-2 7.125673553719011e-2 5.415497520661158e-2 7.378975206611554e-2 2.7305945259173503e-3 6.419826240033085e-3 3.931974029752103e-3 7.686441355646129e-3 3.738938656548464e-3 6.12853976859502e-3 8.767235228762901e-2 6.114686137937469e-2 7.828499069805794e-2
user_003 Sitting 1.446047540852e12 0.537083 -0.650847 9.31124 0.44650772727272725 -0.6856831818181818 9.401814545454545 0.28845814888899995 0.42360181740899994 86.6991903376 9.349398392618532 9.437789541464076 9.057527272727273e-2 3.483618181818182e-2 9.057454545454569e-2 4.782117355371898e-2 5.732195867768597e-2 9.72251239669423e-2 8.203880029619835e-3 1.2135595636694218e-3 8.203748284297563e-3 3.1343671547543177e-3 4.990056541979716e-3 1.4301397123365868e-2 5.598541912636109e-2 7.064033226124942e-2 0.11958844895459539
user_003 Sitting 1.446047540925e12 0.460442 -0.574206 9.46452 0.4848280000000001 -0.6891670000000001 9.454069090909089 0.21200683536400003 0.329712530436 89.5771388304 9.49309529058884 9.492107685859132 2.4386000000000074e-2 0.11496100000000009 1.0450909090911509e-2 4.433761157024795e-2 7.062329752066118e-2 5.478809917355385e-2 5.946769960000036e-4 1.321603152100002e-2 1.0922150082649681e-4 2.8111200184079647e-3 6.5169880832118745e-3 3.972794186626621e-3 5.301999640143296e-2 8.072786435433477e-2 6.303010539913939e-2
user_003 Sitting 1.446047540933e12 0.345482 -0.765807 9.4262 0.4813443636363636 -0.699617909090909 9.450585454545454 0.119357812324 0.586460361249 88.85324643999999 9.463565111181566 9.48928338586127 0.13586236363636361 6.618909090909098e-2 2.4385454545454266e-2 5.098821487603307e-2 7.34735619834711e-2 5.1304462809917434e-2 1.8458581852859497e-2 4.3809957553719095e-3 5.946503933884161e-4 4.1317176202314045e-3 6.804936827912101e-3 3.6694011287753763e-3 6.427843822178168e-2 8.2492040997372e-2 6.057558195160304e-2
user_003 Sitting 1.446047541118e12 0.383802 -0.612526 9.38788 0.443024 -0.6717485454545453 9.46452 0.147303975204 0.375188100676 88.13229089439999 9.415666889301043 9.499323719754216 5.9222e-2 5.9222545454545306e-2 7.664000000000115e-2 5.76385950413223e-2 7.030660330578511e-2 7.632330578512493e-2 3.5072452839999997e-3 3.507309890115685e-3 5.873689600000177e-3 5.4037578223200605e-3 7.833167167294515e-3 9.64789923966959e-3 7.351025657906562e-2 8.850518158443897e-2 9.822372035139776e-2
user_003 Sitting 1.446047541158e12 0.537083 -0.574206 9.50284 0.4674095454545455 -0.6299444545454546 9.474970909090908 0.28845814888899995 0.329712530436 90.30396806560002 9.535310102189914 9.508476174425821 6.967345454545448e-2 5.573845454545456e-2 2.786909090909262e-2 5.9855570247933865e-2 0.10007608264462808 9.089123966942222e-2 4.854390268297512e-3 3.1067753151157044e-3 7.766862280992689e-4 6.554502585894815e-3 1.4869794603729529e-2 1.105123003816697e-2 8.095988257090554e-2 0.12194176726507423 0.10512483074025361
user_003 Sitting 1.446047541175e12 0.460442 -0.689167 9.46452 0.4778605454545454 -0.6194935454545454 9.450585454545454 0.21200683536400003 0.47495115388899994 89.5771388304 9.500741908906535 9.483763584885539 1.741854545454541e-2 6.96734545454546e-2 1.393454545454631e-2 6.523947933884294e-2 8.677486776859503e-2 6.04885950413228e-2 3.0340572575206454e-4 4.8543902682975275e-3 1.9417155702481723e-4 6.91085958427573e-3 1.1449687157067612e-2 5.543818602554532e-3 8.313157994574463e-2 0.10700321096615564 7.445682374742112e-2
user_003 Sitting 1.446047541192e12 0.498763 -0.689167 9.34956 0.4848280000000001 -0.6229772727272729 9.443618181818183 0.24876453016900002 0.47495115388899994 87.41427219360001 9.388183417342145 9.477402355192464 1.393499999999992e-2 6.61897272727271e-2 9.405818181818226e-2 6.492290082644625e-2 8.772497520661153e-2 5.352132231405013e-2 1.9418422499999777e-4 4.381079996437993e-3 8.846941566942232e-3 6.8987275471728005e-3 1.1558912227920352e-2 3.8139265490609105e-3 8.305857901007457e-2 0.10751238174238516 6.1756995952368915e-2
user_003 Sitting 1.4460475412e12 0.498763 -0.689167 9.27292 0.4778607272727273 -0.6369119090909092 9.422716363636365 0.24876453016900002 0.47495115388899994 85.98704532639998 9.311861307518384 9.457088391091498 2.0902272727272686e-2 5.225509090909075e-2 0.14979636363636573 5.5422041322314014e-2 7.91742066115702e-2 6.397223140495938e-2 4.3690500516528754e-4 2.730594525917339e-3 2.243895055867831e-2 5.508618789685197e-3 9.86099776814199e-3 5.74350639699485e-3 7.422006999245688e-2 9.930255670496098e-2 7.578592479474569e-2
user_003 Sitting 1.44604754196e12 0.460442 -0.650847 9.46452 0.44999127272727274 -0.678716 9.44361818181818 0.21200683536400003 0.42360181740899994 89.5771388304 9.49803913885245 9.478809400678257 1.0450727272727278e-2 2.7869000000000033e-2 2.0901818181819465e-2 4.528754545454547e-2 4.148710743801653e-2 1.9951735537190984e-2 1.0921770052892573e-4 7.766811610000018e-4 4.368860033058388e-4 2.986535792406464e-3 2.2738162678332076e-3 5.769984336589671e-4 5.4649206695124714e-2 4.7684549571461905e-2 2.40207916950913e-2
user_003 Sitting 1.446047542413e12 0.422122 -0.765807 9.4262 0.4534750000000001 -0.6821996363636363 9.450585454545454 0.178186982884 0.586460361249 88.85324643999999 9.46667279376091 9.486175161191744 3.1353000000000075e-2 8.360736363636367e-2 2.4385454545454266e-2 2.7235900826446276e-2 2.8819264462809923e-2 2.4702148760330802e-2 9.830106090000048e-4 6.990191254223147e-3 5.946503933884161e-4 1.3062715649120968e-3 1.4066530360563494e-3 1.1032474830954288e-3 3.6142379071003296e-2 3.750537342910146e-2 3.3215169472628446e-2
user_003 Standing 1.446047630907e12 -0.689167 -9.54116 0.344284 -0.8041277272727272 -9.4262 0.4035064545454546 0.47495115388899994 91.0337341456 0.11853147265599999 9.572210652307282 9.470404311628682 0.11496072727272721 0.11495999999999995 5.9222454545454606e-2 8.497683663911854e-2 6.639318273645532e-2 8.869623911845728e-2 1.3215968815074367e-2 1.3215801599999988e-2 3.507299122388437e-3 1.0229017505059551e-2 6.166949670227525e-3 1.3160927524382622e-2 0.10113860541385546 7.852992850007903e-2 0.11472108578802165
user_003 Standing 1.446047631231e12 -0.727487 -9.50284 0.344284 -0.8006440909090909 -9.429683636363636 0.396539 0.529237335169 90.30396806560002 0.11853147265599999 9.536862003480234 9.472512914924552 7.315709090909095e-2 7.315636363636457e-2 5.2254999999999996e-2 6.460626446280994e-2 6.77725619834712e-2 4.845475206611569e-2 5.351959950280998e-3 5.351853540496005e-3 2.7305850249999997e-3 5.803188286028555e-3 5.375021737640885e-3 3.176314455302029e-3 7.617866030607623e-2 7.331453974240638e-2 5.635880104563997e-2
user_003 Standing 1.446047631943e12 -0.842448 -9.38788 0.382604 -0.7971605454545454 -9.40529818181818 0.3860879090909091 0.7097186327039999 88.13229089439999 0.146385820816 9.433366066676305 9.44757028741933 4.5287454545454575e-2 1.741818181818111e-2 3.483909090909121e-3 6.428952066115706e-2 6.365553719008267e-2 5.130495867768594e-2 2.050953539206614e-3 3.0339305785121503e-4 1.2137622553719216e-5 6.695712793529687e-3 5.6033939666416425e-3 3.987201700823439e-3 8.182733524641803e-2 7.485582119409045e-2 6.314429270190172e-2
user_003 Standing 1.446047632979e12 -0.689167 -9.38788 0.305964 -0.7379380909090908 -9.412265454545452 0.3617023636363636 0.47495115388899994 88.13229089439999 9.361396929600001e-2 9.418113187766698 9.448590535195043 4.877109090909082e-2 2.438545454545249e-2 5.5738363636363586e-2 5.415501652892563e-2 3.0085950413224018e-2 6.270585950413224e-2 2.378619308462801e-3 5.946503933883295e-4 3.1067651808594984e-3 4.3258806551938435e-3 1.1749585694966677e-3 4.971305307842974e-3 6.577142734648415e-2 3.427766867067636e-2 7.05074840555453e-2
user_003 Standing 1.446047633237e12 -0.689167 -9.38788 0.382604 -0.7483889999999999 -9.422716363636363 0.36170236363636366 0.47495115388899994 88.13229089439999 0.146385820816 9.420914386040506 9.459752343029551 5.9221999999999886e-2 3.4836363636364e-2 2.0901636363636344e-2 4.750432231404958e-2 3.008595041322434e-2 5.732199173553716e-2 3.5072452839999863e-3 1.213572231404984e-3 4.3687840267768517e-4 3.7378388638985736e-3 1.0999377406462195e-3 4.3214836728707705e-3 6.1137867675431515e-2 3.31653092951991e-2 6.573799261363836e-2
user_003 Standing 1.446047633367e12 -0.804128 -9.34956 0.305964 -0.7449053636363636 -9.422716363636363 0.36866963636363637 0.646621840384 87.41427219360001 9.361396929600001e-2 9.38906321223156 9.459703198070578 5.922263636363634e-2 7.31563636363628e-2 6.270563636363635e-2 4.4337380165289236e-2 3.6736528925621285e-2 5.352162809917354e-2 3.5073206578595012e-3 5.351853540495745e-3 3.931996831768593e-3 3.2524059982727287e-3 1.6526647296770385e-3 4.056701973697217e-3 5.702986935170664e-2 4.065297934564008e-2 6.369224421934916e-2
user_003 Standing 1.446047634532e12 -0.765807 -9.46452 0.305964 -0.7344543636363635 -9.429683636363636 0.3477676363636364 0.586460361249 89.5771388304 9.361396929600001e-2 9.500379632464432 9.465045583166999 3.13526363636365e-2 3.4836363636364e-2 4.1803636363636376e-2 5.225490909090909e-2 3.1669421487604606e-2 5.447188429752066e-2 9.829878069504217e-4 1.213572231404984e-3 1.7475440132231415e-3 4.147163891128476e-3 1.3569944042074078e-3 3.7643580316784374e-3 6.43984773975944e-2 3.683740496027656e-2 6.1354364406115705e-2
user_003 Standing 1.446047634662e12 -0.535886 -9.46452 0.420925 -0.7065850909090909 -9.4262 0.36170236363636366 0.287173804996 89.5771388304 0.177177855625 9.48901946941943 9.460098310075162 0.17069909090909097 3.8320000000000576e-2 5.922263636363634e-2 6.365589256198347e-2 3.451966942148859e-2 5.035481818181819e-2 2.9138179637190103e-2 1.4684224000000442e-3 3.5073206578595012e-3 6.600807368122467e-3 1.6449419972952627e-3 3.3550440600578517e-3 8.124535290170427e-2 4.055788452687421e-2 5.792274216624979e-2
user_003 Standing 1.446047635634e12 -0.765807 -9.38788 0.420925 -0.6543303636363635 -9.419232727272727 0.35125145454545453 0.586460361249 88.13229089439999 0.177177855625 9.4284637726023 9.449174059864886 0.11147663636363647 3.135272727272742e-2 6.967354545454546e-2 6.302253719008266e-2 5.035438016528928e-2 8.265804958677685e-2 1.2427040454950437e-2 9.829935074380258e-4 4.854402936206612e-3 5.892509816134489e-3 4.032369550713747e-3 8.761074538072124e-3 7.676268505031913e-2 6.350094133722545e-2 9.36006118466761e-2
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user_003 Walking 1.446047687546e12 -1.8771 -8.96635 1.30229 -2.5424754545454546 -9.11615 0.152682 3.52350441 80.3954323225 1.6959592440999998 9.252831781492626 9.79489048617874 0.6653754545454547 0.14979999999999905 1.149608 1.3972666942148761 0.45952801652892605 1.826388785123967 0.4427244955115704 2.2440039999999713e-2 1.3215985536639998 2.848263819498798 0.4674070052281754 4.43694763761664 1.687680010991064 0.683671708664455 2.1064063325048754
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user_003 Walking 1.446047689099e12 -4.78944 -11.15061 1.11069 -1.6820099090909089 -9.286850909090909 1.4033162727272726 22.938735513599998 124.33610337210001 1.2336322760999998 12.18640517797599 9.603071921107578 3.107430090909091 1.8637590909090918 0.2926262727272726 1.4004335206611571 0.6150263636363636 1.4010657520661156 9.65612176988728 3.473597948946284 8.563013549025612e-2 2.525419334934868 0.6853445784876789 2.4557176957492683 1.5891567999838367 0.8278554091673732 1.5670729707800044
user_003 Walking 1.446047689423e12 -2.2603 -7.39522 -0.958607 -2.3439056363636364 -9.23807909090909 0.2850610909090909 5.1089560899999995 54.6892788484 0.918927380449 7.792121811089006 9.686183649343109 8.360563636363638e-2 1.8428590909090907 1.243668090909091 1.0967207190082644 0.9507247933884297 1.283254867768595 6.989902431768598e-3 3.39612962894628 1.5467103203454629 1.9360527094687148 1.2617876186290011 1.9974827090385192 1.3914211114787338 1.123293202431583 1.4133232853945763
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user_003 Walking 1.446047692724e12 -2.37526 -9.08132 0.650847 -3.1904381818181817 -8.760819090909091 -0.9829931818181816 5.6418600676 82.47037294239999 0.42360181740899994 9.40934826794125 9.711024072087437 0.8151781818181818 0.32050090909090834 1.6338401818181816 1.1299748760330577 0.9947448760330573 1.8054882066115703 0.6645154681123967 0.10272083272809869 2.6694337397236687 3.8177683449762583 1.624831435103606 4.349292087728119 1.9539110381427958 1.2746887600915002 2.085495645578796
user_003 Walking 1.446047694212e12 -1.68549 -8.39155 0.995729 -3.0232225454545447 -8.931517272727273 -0.272325 2.8408765400999996 70.4181114025 0.991476241441 8.616870904454878 9.798154136854562 1.3377325454545448 0.5399672727272726 1.268054 1.7348647107438018 0.6739317355371907 1.7291648925619834 1.7895283631682957 0.29156465561652883 1.6079609469160001 5.105803910511268 0.6571788245633365 3.537602261767337 2.259602600129339 0.8106656675617493 1.8808514725430439
user_003 Walking 1.446047694665e12 -2.87342 -9.31124 -1.26517 -2.444933818181818 -9.474969999999999 0.41395727272727273 8.2565424964 86.6991903376 1.6006551288999997 9.826311004792185 9.933644266781107 0.42848618181818177 0.16372999999999927 1.6791272727272726 1.1565773719008263 0.6859657024793389 1.47200647107438 0.18360040800912392 2.680751289999976e-2 2.8194683980165283 1.6581222852926367 1.0010658402313288 2.4672273237565943 1.287680971860902 1.000532778189365 1.5707410110379731
user_003 Walking 1.446047695248e12 -3.25663 -8.65979 0.727487 -3.033673545454545 -9.036027272727273 -1.1223383636363635 10.6056389569 74.99196284409999 0.529237335169 9.28045468369783 9.887957901050113 0.22295645454545499 0.37623727272727336 1.8498253636363635 1.4678886198347103 1.2683712396694213 1.649039 4.9709580623479535e-2 0.1415544853892567 3.4218538759524044 4.119139327655233 2.252980369876934 3.138702060940305 2.029566290529884 1.500993127857997 1.7716382421195094
user_004 Jogging 1.446046318092e12 5.59536 -5.47921 4.55952 5.389392875 -5.934259999999999 -1.1645778749999995 31.308053529600002 30.021742224100002 20.7892226304 9.061954446150125 12.216535243673478 0.20596712499999992 0.45504999999999907 5.724097875 5.715480538541667 4.204357976190476 2.761588395684523 4.242245658076559e-2 0.20707050249999914 32.765296482579515 52.835246199173355 33.24591593153357 13.561606868199032 7.2687857444812165 5.765927152811902 3.6826087041931337
user_004 Jogging 1.446046319776e12 0.575403 0.920286 -2.4531 7.037601 -5.81712190909091 -0.8889327272727272 0.331088612409 0.8469263217960001 6.01769961 2.682482906600711 12.387770865882652 6.462198000000001 6.73740790909091 1.5641672727272729 6.405192909090909 5.481706280991736 3.3021975289256202 41.76000299120401 45.39266533348075 2.4466192570710747 61.41928641993893 42.6502568591944 14.266236440739085 7.837045771203517 6.530716412400281 3.777067174507105
user_004 Jogging 1.446046320682e12 15.40536 -14.7144 -4.9056 5.773029999999999 -4.29127709090909 -0.7077829999999999 237.3251167296 216.51356736 24.064911359999996 21.86100627715019 11.59551959765128 9.63233 10.42312290909091 4.197817 7.104774851239669 5.092802545454545 2.930712619834711 92.78178122889999 108.64149117801576 17.621667565489 68.18608075165695 45.272654416877344 13.356822954340474 8.257486345835332 6.728495702374889 3.6546987501489743
user_004 Jogging 1.44604632094e12 -7.89339 -0.229323 6.89706 5.720775454545455 -4.859112818181817 -0.33851381818181814 62.3056056921 5.2589038329e-2 47.5694366436 10.484637875197645 12.382847689240384 13.614165454545455 4.629789818181817 7.235573818181818 7.7625545206611575 5.522876561983471 3.032688570247934 185.34550102373888 21.434953760540022 52.35352847835821 85.137659610978 47.519657698112105 15.47308031707065 9.227007077648635 6.893450347838309 3.9335836481598623
user_004 Jogging 1.44604632107e12 8.50771 -12.98999 2.18366 6.323450000000002 -5.085551 -1.3731619999999998 72.3811294441 168.73984020010002 4.768370995600001 15.680859052991964 12.889850411129373 2.1842599999999974 7.904439000000001 3.556822 7.966191876033057 5.821204644628099 2.5582766694214873 4.770991747599989 62.480155904721016 12.650982739684 87.93005493205713 47.961374134025576 11.119942162986327 9.377102693905892 6.925415087489383 3.3346577280114262
user_004 Jogging 1.4460463223e12 7.62634 -1.11069 -7.7239e-2 6.981861818181819 -5.113419999999999 -0.8053254545454547 58.1610617956 1.2336322760999998 5.965863121e-3 7.707182360293611 13.166977051043297 0.6444781818181813 4.002729999999999 0.7280864545454546 7.87466743801653 5.880742809917354 2.431282611570248 0.4153521268396687 16.02184745289999 0.5301098852925703 96.87531135707144 50.59894899318002 9.012174346215128 9.8425256594571 7.113293821653933 3.002028371987035
user_004 Jogging 1.446046322495e12 12.4547 -8.73643 -4.40743 5.699873636363636 -4.232053636363636 -1.1153708181818183 155.11955209 76.3252091449 19.425439204899998 15.838882550224305 12.631746355363127 6.754826363636365 4.504376363636364 3.2920591818181815 8.404817429752066 5.924762809917355 2.7349940082644633 45.62767920287688 20.289406425285957 10.837653656593394 99.4303642243738 46.63110414598136 12.545256132475203 9.971477534667258 6.828697104571366 3.5419283070772627
user_004 Jogging 1.446046322818e12 2.22318 4.714 -0.690364 6.887803636363637 -5.479206363636364 -0.9342202727272728 4.9425293124000005 22.221796000000005 0.476602452496 5.257464005097515 13.652307201253643 4.664623636363637 10.193206363636364 0.24385627272727284 7.565568826446282 6.1325166942148766 3.4842991157024787 21.758713668922322 103.90145597167687 5.9465881748438074e-2 85.44219569961149 49.359338763878434 17.138670611506832 9.243494777388664 7.025620169342948 4.139887753491251
user_004 Jogging 1.446046323919e12 -12.14694 3.90927 0.152682 8.263850909090909 -4.988009090909092 -1.6344380000000003 147.54815136360003 15.282391932899998 2.3311793124000002e-2 12.761420574905602 13.32878135637509 20.41079090909091 8.897279090909091 1.7871200000000003 7.503497272727272 5.000009421487603 2.6817890330578518 416.6003855346281 79.1615752215281 3.1937978944000007 83.64378627905913 43.36608320371898 10.340309980211263 9.145697692306427 6.585292947448806 3.215635237431519
user_004 Jogging 1.446046324307e12 3.14286 -4.06135 -2.41478 7.974707272727273 -5.670806363636364 -0.7391351818181818 9.877568979600001 16.4945638225 5.8311624484 5.674794732014543 13.21582437877326 4.831847272727273 1.6094563636363644 1.675644818181818 7.802776611570248 4.166146611570248 3.0396570413223145 23.34674806696199 2.5903497864495892 2.807785556699578 88.72848169522757 33.40847150884982 14.554685959196457 9.419579698438119 5.7800061858833525 3.8150604135709902
user_004 Jogging 1.446046326574e12 12.0715 -5.70913 -2.29982 7.38248581818182 -5.493142727272727 -0.5266323636363637 145.72111225 32.5941653569 5.2891720324 13.55007194221861 13.15136563242288 4.68901418181818 0.21598727272727292 1.7731876363636363 7.681798446280993 5.468403966942149 2.036678347107438 21.98685399729202 4.665050198016537e-2 3.1441943937528594 85.34078258003082 48.436344589920964 6.831764064025652 9.238007500539865 6.959622445932032 2.6137643474547687
user_004 Jogging 1.446046326639e12 1.61005 0.268841 -2.8363 7.281459454545455 -6.033110818181819 -0.7112664545454546 2.5922610025 7.2275483281e-2 8.04459769 3.2724813484237 12.828283111638287 5.671409454545455 6.301951818181819 2.1250335454545457 7.794859388429751 5.05574826446281 2.2292298016528926 32.16488520110758 39.71459671868514 4.515767569307116 86.48260182948019 41.36213986419955 7.242283975172693 9.299602240390724 6.431340440701265 2.6911491922917787
user_004 Jogging 1.44604632761e12 15.32872 -14.67608 -5.0972 5.4734360909090904 -3.793111272727273 -0.34896536363636366 234.96965683840003 215.38732416640002 25.98144784 21.8251787815083 11.905846007617221 9.855283909090911 10.882968727272727 4.7482346363636365 7.350532371900827 5.82310479338843 3.0558068677685952 97.12662092878622 118.43900831879617 22.545732161963315 77.70046956614337 45.631422866974525 15.833528605261323 8.814786983594292 6.755103468265643 3.9791366658185194
user_004 Jogging 1.446046327869e12 -10.65245 4.13919 5.36425 6.501117909090909 -4.55603409090909 -0.4186382727272728 113.4746910025 17.1328938561 28.7751780625 12.624688626698878 12.71974471624847 17.15356790909091 8.69522409090909 5.782888272727273 7.723284404958677 6.096096619834711 2.903793123966942 294.24489201179347 75.6069219911258 33.441796774846615 82.30222588031641 49.14387324683357 13.352193441058244 9.072057422675211 7.010269127988852 3.654065330704727
user_004 Jogging 1.446046327934e12 12.22478 -6.05401 -4.63736 6.678785181818182 -3.8593013636363636 -1.0247964545454544 149.4452460484 36.6510370801 21.505107769600002 14.408379190530072 12.460816653562178 5.545994818181819 2.1947086363636363 3.6125635454545457 7.868965173553719 5.46998726446281 2.945280504132232 30.75805852329958 4.816745998529132 13.050615369947117 83.68466370606724 42.08347585402162 13.633011805578548 9.147932209306497 6.487177803484472 3.6922908614542473
user_004 Jogging 1.446046328581e12 -3.17999 -1.68549 -0.1922 8.981486363636364 -6.047043636363636 -1.160660090909091 10.1123364001 2.8408765400999996 3.694084e-2 3.604185591808502 13.103828097993564 12.161476363636364 4.361553636363636 0.9684600909090909 6.4954519752066116 5.569113595041323 2.5399093471074377 147.90150734328597 19.02315012287686 0.9379149476836446 54.42817332005659 46.03700027441227 9.23046015355527 7.377545209624715 6.785057131256322 3.0381672359426286
user_004 Jogging 1.446046328905e12 19.50564 -5.67081 1.03405 7.100308181818182 -4.7511209090909094 -0.4221227272727273 380.4699918096 32.158086056100004 1.0692594024999997 20.33955105866892 13.054363658769024 12.405331818181818 0.9196890909090909 1.4561727272727272 8.1137726446281 5.9206470247933884 2.656452793388429 153.8922575191942 0.84582802393719 2.120439011652892 88.05080876348978 50.20722639022751 9.792734096364068 9.383539245055129 7.08570577925922 3.1293344494259587
user_004 Jogging 1.446046329617e12 3.56439 -7.05034 6.05401 5.84618909090909 -4.925304545454545 -0.7042981818181816 12.7048760721 49.70729411560001 36.6510370801 9.953050148964387 12.291283422299722 2.28179909090909 2.125035454545455 6.758308181818181 6.877387685950413 6.140116363636364 2.6222487603305784 5.20660709127355 4.5157756830752085 45.67472948043057 77.1762593682838 52.764850806034104 10.386124266575505 8.785001956077403 7.263941822869598 3.2227510401170467
user_004 Jogging 1.446046329683e12 19.00747 -7.08866 -0.1922 6.992314545454545 -4.904402727272727 -0.44650727272727264 361.28391580090005 50.2491005956 3.694084e-2 20.28718702128267 13.209857240769736 12.015155454545457 2.1842572727272733 0.2543072727272726 7.863264297520661 6.199972148760332 2.42336347107438 144.36396059689346 4.770979833461986 6.467218896198342e-2 90.17570123666434 52.98692180883688 9.849859374475129 9.496088733613663 7.279211620006447 3.1384485617061064
user_004 Jogging 1.446046330071e12 17.05314 -7.05034 -3.75599 7.476543181818181 -5.385147272727274 -0.7356514545454546 290.80958385959997 49.70729411560001 14.107460880100001 18.831472031025616 13.604796241409561 9.576596818181818 1.6651927272727267 3.0203385454545457 6.897656694214876 5.849389256198347 2.7007900661157027 91.71120661801011 2.7728668189619814 9.122444929158481 82.83997545198206 51.75787714759219 10.641467584078235 9.101646853838158 7.194294763741071 3.2621262366864707
user_004 Jogging 1.446046330265e12 4.02423 -3.52487 -1.76333 6.295580454545455 -4.420171818181819 -1.073566909090909 16.1944270929 12.424708516899999 3.1093326889000004 5.632802881221745 11.50053752911144 2.2713504545454546 0.8953018181818191 0.689763090909091 6.918558636363636 5.134288347107438 2.0914646446280996 5.159032887363844 0.8015653456396711 0.475773121580463 77.31788883703922 43.5971327069604 7.869029743331553 8.793059128485332 6.602812484612932 2.8051790929157363
user_004 Jogging 1.446046330329e12 12.18646 -8.04667 4.48288 7.079405 -4.510747272727273 -1.2163969090909088 148.5098073316 64.7488980889 20.0962130944 15.27595884109734 11.984438319305344 5.107055 3.5359227272727276 5.699276909090909 7.175400082644629 5.26255082644628 1.995189074380165 26.082010773024997 12.502749533243804 32.48175728649682 79.21565280810752 44.32322123879391 6.669668634792123 8.900317567823494 6.657568718293031 2.582570160671753
user_004 Jogging 1.446046330848e12 16.01849 -5.05768 -2.33814 8.019996363636364 -5.001943636363635 -0.8088077272727273 256.5920218801 25.580126982400003 5.466898659600001 16.95992474989497 12.894361379172755 7.998493636363635 5.573636363636503e-2 1.529332272727273 6.6452502066115695 5.332539917355372 2.045543966942149 63.975900450949574 3.1065422314051137e-3 2.3388572004051658 71.60663987257274 44.567811622551844 7.075141314559144 8.462070661048202 6.675912793210517 2.6599137795348073
user_004 Jogging 1.446046331495e12 8.62267 -8.96635 -0.460442 6.427961 -3.901106363636364 -0.32458081818181816 74.35043792889999 80.3954323225 0.21200683536400003 12.448207786133874 11.40122148597141 2.1947089999999996 5.065243636363636 0.13586118181818185 6.147401809917355 4.683945950413223 1.9023978347107438 4.816747594680998 25.65669309572231 1.845826072503307e-2 68.3485394276605 34.49821943043216 5.597293831373793 8.267317547285849 5.873518488132318 2.3658600616633674
user_004 Jogging 1.446046331561e12 18.04947 -17.93331 -5.40376 6.612595545454545 -5.071618181818182 -0.6032735454545455 325.7833672809 321.6036075561 29.2006221376 26.01129748733423 12.22407355301134 11.436874454545453 12.861691818181818 4.800486454545455 6.45998188429752 5.848123719008263 2.1997754876033055 130.80209728903435 165.42311642588513 23.044670200274393 74.42364823112277 49.53640214712795 7.47964046772554 8.626914177799774 7.038210152242398 2.734893136436146
user_004 Jogging 1.44604633318e12 18.31771 -7.47186 -3.10454 7.713432727272728 -4.754604545454545 -0.7042989090909091 335.53849964410006 55.828691859600006 9.638168611600001 20.02511822974586 13.149988530002542 10.604277272727273 2.7172554545454553 2.400241090909091 6.938827685950414 5.259700247933884 3.0469385041322314 112.45069647688018 7.383477205257028 5.761157294488465 77.11467456979197 48.156471003066486 12.895906901866105 8.78149614643154 6.939486364498923 3.5910871476289885
user_004 Jogging 1.446046334476e12 6.13185 -5.93905 -3.0279 7.685562727272727 -6.245612363636363 -0.4499909090909093 37.5995844225 35.2723149025 9.16817841 9.05759779052923 13.862535036033972 1.5537127272727274 0.30656236363636324 2.5779090909090905 7.415138760330578 5.167541801652892 3.0304713057851242 2.4140232388892566 9.398048279831381e-2 6.645615280991733 82.42637556285928 43.10521410638309 12.187500293637099 9.078897265794964 6.565456123254735 3.4910600529978137
user_004 Jumping 1.446046440753e12 19.54396 -19.58108 -6.89825 4.1884622857142855 -2.999333571428571 -1.5224617142857144 381.96637248159993 383.4186939664 47.5858530625 28.512644905559004 7.446083883383553 15.355497714285713 16.581746428571428 5.375788285714286 3.529288130612245 4.4176791921768706 1.270878112244898 235.79131005343376 274.9543146214413 28.899099692822944 40.42154505965868 49.56948207287595 4.601596063441028 6.357794040361695 7.040559784056659 2.14513311089103
user_004 Jumping 1.446046441725e12 0.767005 1.30349 1.03405 3.717668909090908 -2.779365454545454 -0.7217180909090909 0.5882966700250001 1.6990861801000001 1.0692594024999997 1.832114148361122 6.847435681349492 2.950663909090908 4.082855454545454 1.7557680909090907 4.667160314049585 5.080450140495867 1.426719958677686 8.706417504411638 16.669708662711567 3.082721589054553 34.66505868718512 41.30950542823461 3.54571694005584 5.887704025100542 6.427247111184897 1.8830074190124264
user_004 Jumping 1.446046441855e12 19.50564 -19.58108 -6.28513 6.448862999999999 -5.51752609090909 -1.188529 380.4699918096 383.4186939664 39.5028591169 28.34416244825202 10.589792564338788 13.056777 14.06355390909091 5.096601 6.050492041322314 6.463148644628098 1.8384256611570249 170.479425627729 197.7835485539062 25.975341753200997 53.52722088151006 62.083623176617515 5.872172381026635 7.31622996368417 7.879316161737484 2.423256565249878
user_004 Jumping 1.446046442243e12 0.575403 1.15021 -0.690364 3.6410292727272737 -2.856005545454545 -0.826227181818182 0.331088612409 1.3229830441 0.476602452496 1.4596828796026209 7.0567311800225605 3.0656262727272736 4.006215545454545 0.13586318181818202 4.304226818181818 5.246715801652892 1.354511909090909 9.398064444035716 16.049762996641654 1.8458804173760387e-2 29.45904764510686 39.08100872537067 3.7849847946391066 5.427618966462814 6.251480522673862 1.9455037380172537
user_004 Jumping 1.446046442372e12 18.16443 -17.3585 1.60885 5.591881181818182 -4.914851 -0.906352 329.9465172249 301.31752224999997 2.5883983225 25.17642623164376 9.544468036485442 12.572548818181819 12.443649 2.515202 5.156457942148761 5.815502611570248 1.753866247933884 158.06898378556505 154.844400435201 6.326241100803999 42.76716719331571 50.12337746871192 4.928973948004476 6.539661091625139 7.079786541182716 2.2201292638052577
user_004 Jumping 1.446046443215e12 -0.880768 -0.612526 -1.91661 4.623420909090909 -3.2287572727272735 -1.8016529999999997 0.775752269824 0.375188100676 3.6733938920999996 2.196436719461774 8.431501330251807 5.504188909090908 2.6162312727272736 0.1149570000000002 6.099263876033058 4.956621512396695 1.8605928016528923 30.296095546959364 6.84466607239617 1.3215111849000045e-2 44.71450237822124 32.7193750866241 6.223155739080556 6.686890336936986 5.720085234209723 2.494625370487632
user_004 Jumping 1.446046444575e12 0.881966 -4.94272 3.79311 6.790261454545456 -6.263030272727272 -0.8749987272727274 0.7778640251560001 24.430480998399997 14.387683472099999 6.292537524374089 11.126299442112229 5.908295454545455 1.3203102727272729 4.6681087272727275 6.9910826033057845 6.443830049586777 1.6366885537190081 34.90795517820249 1.7432192162691655 21.791239089639802 58.32619930429955 59.72487196810328 3.9530999690558626 7.637159112150247 7.728186848679532 1.9882404203354942
user_004 Jumping 1.446046444769e12 0.268841 -1.95374 3.7722e-2 3.2195042727272734 -2.3926784545454542 -0.9725412727272725 7.2275483281e-2 3.8170999876000002 1.422949284e-3 1.9725106894932154 7.197199404975865 2.9506632727272732 0.4389384545454542 1.0102632727272725 5.604267272727273 5.468403644628099 1.521094487603306 8.706413749021623 0.1926669668787518 1.0206318802216192 38.98070197949247 47.5268644494463 3.7172557078802515 6.243452729018814 6.893973052561658 1.9280185963522891
user_004 Jumping 1.446046445287e12 0.11556 -1.11069 0.382604 3.397171909090909 -2.2568159090909092 -0.9237708181818182 1.3354113599999998e-2 1.2336322760999998 0.146385820816 1.180411881724341 7.075012334908058 3.281611909090909 1.1461259090909093 1.3063748181818182 4.881565661157025 5.449401462809918 1.427669438016529 10.768976721887281 1.3136045994894632 1.7066151655795787 33.09439934785701 45.55143298526623 2.6018435675532396 5.752773187590226 6.749180171344237 1.6130231143890157
user_004 Jumping 1.446046445611e12 2.8363 -10.65245 1.80046 6.518536181818181 -6.203808181818181 -0.9899598181818184 8.04459769 113.4746910025 3.2416562115999996 11.16964390229608 10.831203183334122 3.682236181818181 4.448641818181819 2.7904198181818183 6.020091264462809 6.157535694214877 1.3522956859504134 13.558863298690936 19.790414026476036 7.786442761701852 50.54368804665865 54.31564822609823 2.9312400316853586 7.1094084174886625 7.36991507590815 1.712086455669035
user_004 Jumping 1.44604644574e12 -0.765807 2.33814 -1.64837 3.5330348181818176 -2.9117445454545456 -0.8122925454545453 0.586460361249 5.466898659600001 2.7171236568999997 2.9615000722183007 7.545395689822752 4.298841818181818 5.249884545454545 0.8360774545454546 4.913235181818182 5.647971008264463 1.154676611570248 18.480040977748757 27.561287740602477 0.6990255099992067 32.672137932914204 43.8247559736747 2.23586034254455 5.715954682545533 6.620026886174609 1.495279352677803
user_004 Jumping 1.446046446387e12 1.30349 -1.57053 -1.76333 3.4668452727272734 -2.702724454545454 -0.9307371818181818 1.6990861801000001 2.4665644809 3.1093326889000004 2.6972177053215414 6.522886174272082 2.1633552727272733 1.132194454545454 0.8325928181818183 4.403352826446281 4.768820842975207 1.425451826446281 4.680106036036896 1.2818642829034783 0.6932108008879423 29.814088068487422 33.13063707336669 2.8420858909499063 5.460227840345806 5.755921913418101 1.6858487153211306
user_004 Jumping 1.446046446712e12 -2.10702 -2.18366 4.06135 5.431632909090909 -5.245799181818182 -0.7913907272727272 4.439533280399999 4.768370995600001 16.4945638225 5.069760161832116 9.726178424784191 7.538652909090908 3.0621391818181816 4.852740727272727 6.073928570247935 6.269962735537191 2.0376260165289257 56.83128768374481 9.376696368826122 23.54909256613144 51.70801020713879 53.619849938282414 5.52751424180559 7.190828200363209 7.322557609079113 2.3510666179003925
user_004 Jumping 1.446046447294e12 0.690364 6.13185 -2.41478 4.372599 -3.9324581818181814 -0.8088090909090909 0.476602452496 37.5995844225 5.8311624484 6.626262092869252 9.25374689473398 3.6822350000000004 10.06430818181818 1.605970909090909 5.767999487603306 6.21485658677686 1.7959872231404963 13.558854595225002 101.29029917861237 2.5791425608462806 46.44946369914939 57.41211919025554 6.140247961835453 6.815384339796942 7.577078539269309 2.477952372794008
user_004 Jumping 1.446046447618e12 14.94552 -13.18159 -4.67568 4.574651181818182 -3.8662689090909086 -1.0700833636363638 223.36856807040002 173.7543149281 21.861983462399998 20.469119826238256 8.255475939941938 10.370868818181819 9.31532109090909 3.605596636363636 5.605217123966942 5.653037636363636 1.7095292644628097 107.55492004393595 86.77520702673573 13.000327104156765 46.00866792942744 48.25952326499671 5.097796350635938 6.782968961260802 6.946907460517717 2.2578300092424888
user_004 Jumping 1.446046449302e12 19.08411 -17.97163 -4.06255 6.292096636363637 -5.238832727272728 -1.3313578181818182 364.2032544921 322.97948485690006 16.5043125025 26.527100328748713 10.742951779313438 12.79201336363636 12.732797272727273 2.731192181818182 6.28168061983471 6.237977859504133 1.770017694214876 163.63560589545125 162.12412638837108 7.459410734024761 57.181595329683844 55.44002913204303 5.704743067659652 7.561851316290466 7.445806143866696 2.3884603969209226
user_004 Jumping 1.446046449884e12 9.77228 -10.88237 0.305964 6.661365181818183 -5.935567 -1.4289012727272727 95.4974563984 118.4259768169 9.361396929600001e-2 14.629321487498865 10.730218018448529 3.1109148181818176 4.946803 1.7348652727272729 5.927614074380164 5.7094111404958685 1.4390697024793389 9.677791005983211 24.470859920809 3.009757514515075 50.27496977080698 50.6429279554915 3.326290719735871 7.090484452476218 7.1163844721523795 1.823812139376167
user_004 Jumping 1.446046449949e12 -2.0687 0.575403 1.07237 5.222611545454545 -4.946205818181818 -1.0387312727272728 4.279519690000001 0.331088612409 1.1499774169 2.4001220217541026 9.358456768935065 7.291311545454546 5.521608818181818 2.111101272727273 5.7591315454545455 5.5906493801652895 1.4365365619834711 53.16322405287876 30.488163941023213 4.456748583710711 47.505802565996596 49.17626807639828 3.315524702677734 6.892445325571803 7.012579274161418 1.8208582324491203
user_004 Jumping 1.446046450273e12 1.03525 0.996927 -2.33814 3.6863156363636365 -2.5598956363636356 -1.1815612727272728 1.0717425625 0.993863443329 5.466898659600001 2.7445408842698993 6.7919229626582425 2.6510656363636365 3.5568226363636355 1.1565787272727273 4.373900206611571 4.6421415041322325 1.104005090909091 7.028149008308133 12.650987266548762 1.3376743523798016 30.204080410236873 35.12321301457914 2.2349330079064456 5.495823906407198 5.926484034786489 1.4949692330969375
user_004 Jumping 1.446046450403e12 15.2904 -16.4005 -3.44943 6.609110272727273 -5.649906818181818 -1.5125094545454545 233.79633216 268.97640025000004 11.8985673249 22.686368147742378 10.73749835209278 8.681289727272727 10.750593181818182 1.9369205454545455 5.950099537190083 6.178438495867769 1.3551456363636365 75.36479132885098 115.57525376095559 3.751661199403934 52.523254056726394 57.86450307308849 2.7311461983206873 7.247292877807989 7.6068720952234035 1.6526179831772034
user_004 Jumping 1.446046450531e12 0.422122 6.63001 -3.37279 3.9545577272727273 -3.2078577272727276 -0.9237703636363637 0.178186982884 43.95703260010001 11.375712384100002 7.450565882339677 8.460411268528444 3.5324357272727274 9.837867727272728 2.4490196363636363 5.265083752066116 5.7806671487603305 1.6712091074380166 12.478102167312802 96.78364141931428 5.997697179294677 39.42287793470751 48.03158359135643 4.1075853388824015 6.278764045153115 6.9304822048221455 2.0267178735291207
user_004 Jumping 1.446046450921e12 19.54396 -18.12491 -4.9056 6.191071363636365 -5.245801363636364 -1.7528832727272723 381.96637248159993 328.5123625081 24.064911359999996 27.10246568763993 10.580288705372087 13.352888636363634 12.879108636363636 3.1527167272727272 6.375738710743801 6.294983049586777 1.9831561570247935 178.29963493512906 165.8714392672564 9.939622762425255 57.35020530279037 57.54984604088095 5.6981677095347285 7.572991833006977 7.586161482652538 2.3870835154084427
user_004 Jumping 1.446046451179e12 -0.689167 -1.41725 -0.537083 3.553937181818182 -2.316038363636364 -1.435869 0.47495115388899994 2.0085975625 0.28845814888899995 1.6649344927888305 7.489633255365871 4.2431041818181825 0.898788363636364 0.8987860000000001 4.800173760330579 5.271100983471074 1.8400087190082643 18.003933097762946 0.807820522608133 0.8078162737960002 35.33453433582328 40.798926170358726 4.5008850493141415 5.944285855830226 6.387403711239703 2.1215289414274183
user_004 Jumping 1.446046451309e12 5.99e-4 2.22318 -0.613724 3.790826000000001 -3.0301892727272732 -1.1258224545454545 3.5880100000000004e-7 4.9425293124000005 0.37665714817600005 2.306336232941112 7.049070078541021 3.790227000000001 5.253369272727273 0.5120984545454544 4.614273231404958 4.632957049586778 1.697811479338843 14.36582071152901 27.597888715635076 0.26224482714784286 34.150457092262734 33.510629728040335 4.005569173775021 5.843839242506824 5.788836647206443 2.0013918091605705
user_004 Jumping 1.446046451762e12 0.920286 -2.41358 0.344284 3.5051649090909085 -2.3717772727272726 -1.3940651818181817 0.8469263217960001 5.8253684164 0.11853147265599999 2.6059213746488976 7.351790595676024 2.5848789090909086 4.180272727272749e-2 1.7383491818181818 5.23436547107438 4.90373214876033 1.4349531900826447 6.681598974663006 1.7474680074380348e-3 3.021857877927942 39.88697797769975 39.20278665489539 2.894475197684697 6.315613824300829 6.2612128741079704 1.7013157254562414
user_004 Jumping 1.446046451892e12 -0.382604 0.690364 7.6042e-2 3.557419909090909 -2.660921272727273 -1.2129147272727272 0.146385820816 0.476602452496 5.782385764e-3 0.7929506031752546 6.9635497729535 3.9400239090909093 3.3512852727272726 1.2889567272727271 5.185593942148761 4.676977388429751 1.325692917355372 15.523788404208009 11.23111297919871 1.6614094447816194 39.5295646746675 36.15230679208021 2.620653828008208 6.287254144272164 6.0126788365985595 1.6188433611712432
user_004 Jumping 1.446046452021e12 19.54396 -19.08292 -7.43474 6.243325454545455 -5.102970363636363 -1.8922294545454543 381.96637248159993 364.15783572640004 55.2753588676 28.30900152028679 10.349931781329445 13.300634545454542 13.979949636363639 5.542510545454546 6.506536148760332 5.7812990247933875 1.7316982231404958 176.90687931173878 195.43899183526383 30.719423146474846 58.50151760448834 53.12020252076061 5.359819226407735 7.648628478654741 7.288360756765584 2.315128339079226
user_004 Jumping 1.446046452538e12 18.54763 -15.40417 -3.98591 4.9648212727272725 -3.9847141818181813 -1.3940644545454548 344.01457861690005 237.28845338890002 15.8874785281 24.437481673321006 8.936126658691224 13.58280872727273 11.41945581818182 2.5918455454545453 5.416781504132231 5.744247553719009 1.6895778347107437 184.49269292167622 130.4039711834066 6.717663331492569 45.55107155931277 48.760047922413534 5.977856426539219 6.749153395746222 6.982839531480981 2.444965526656607
user_004 Jumping 1.446046452993e12 0.613724 2.10822 -1.38013 3.665413818181818 -2.7480122727272733 -1.157175909090909 0.37665714817600005 4.444591568400001 1.9047588169000003 2.5934547486848505 7.334066225954348 3.051689818181818 4.856232272727274 0.22295409090909102 4.790039247933884 5.016162074380166 1.2848392396694217 9.312810746394577 23.582991886677906 4.970852665309922e-2 36.88789352842561 41.51884982458453 3.4438666456618092 6.073540444289937 6.443512227394662 1.8557657841607624
user_004 Jumping 1.446046453445e12 3.0279 -1.45557 -7.7239e-2 3.675864363636364 -2.6922731818181824 -1.1362745454545455 9.16817841 2.1186840249000003 5.965863121e-3 3.3604803671530354 7.688581707506595 0.6479643636363641 1.2367031818181824 1.0590355454545455 5.11655426446281 4.447690247933884 1.4346366611570247 0.4198578165426783 1.5294347599192164 1.1215562865362068 38.29682912226736 35.61574287410279 4.090531801082638 6.1884431905179 5.967892666101058 2.0225063166978337
user_004 Jumping 1.44604645351e12 -7.6042e-2 0.11556 -1.26517 3.8639823636363633 -2.8873586363636368 -1.0631172727272726 5.782385764e-3 1.3354113599999998e-2 1.6006551288999997 1.2727103473548094 7.464115552925086 3.9400243636363634 3.0029186363636367 0.20205272727272727 4.969606842975207 4.325445000000001 1.371297 15.523791986048131 9.017520336620043 4.082530459834711e-2 36.90134728909755 34.7171749005811 4.02080485908967 6.0746479148258095 5.892128214879671 2.005194469144993
user_004 Jumping 1.446046453704e12 19.54396 -17.70339 -8.46939 6.215456545454546 -4.782473272727273 -1.665791818181818 381.96637248159993 313.41001749209994 71.73056697210001 27.69669577667704 10.319630313832954 13.328503454545451 12.920916727272726 6.803598181818183 6.116683256198346 5.222330438016529 1.9416679917355373 177.64900433783004 166.95008907311612 46.288948219639686 53.542354201833035 48.31052397701225 8.222915800069886 7.3172641199995665 6.950577240561553 2.8675626933111484
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user_004 Jumping 1.44604645487e12 12.22478 -14.1396 -1.03525 6.717105181818181 -6.022658545454546 -1.592634181818182 149.4452460484 199.92828816 1.0717425625 18.720183673535363 11.750544288016998 5.50767481818182 8.116941454545454 0.557384181818182 6.046375016528926 6.576525785123966 1.9524353471074383 30.334481902834142 65.88473857651847 0.3106771261411241 55.06290521812116 67.83194182478591 6.36341218656381 7.420438344068439 8.236014923783584 2.522580461861189
user_004 Jumping 1.446046454999e12 1.11189 5.2888 -2.49142 3.543486090909091 -2.371778181818182 -0.9168032727272727 1.2362993721000002 27.97140544 6.207173616400001 5.951040113165093 8.1335275932362 2.431596090909091 7.660578181818182 1.5746167272727276 4.734616950413223 5.498490280991735 2.0813304214876034 5.912659549324371 58.684458079748765 2.4794178378070755 34.00437737975152 47.93823792689663 7.181088815206571 5.831327239981608 6.923744501849893 2.679755364806006
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user_004 Jumping 1.446046455906e12 19.54396 -18.43147 -6.89825 5.710325181818182 -4.698866090909092 -1.634437181818182 381.96637248159993 339.7190863609 47.5858530625 27.735740695085102 9.91661877902701 13.833634818181817 13.732603909090908 5.263812818181818 5.815186834710744 5.599832173553719 1.9872717603305785 191.3694522828123 188.5844101239789 27.707725384855213 50.6927278488261 52.74739577233272 6.313621098201948 7.119882572685177 7.262740238527929 2.5126920022561356
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user_004 Jumping 1.446046456423e12 15.78857 -13.10495 -5.59536 4.7453508181818185 -3.9289750909090913 -1.4672216363636366 249.2789426449 171.73971450250002 31.308053529600002 21.267973826319235 8.458796354972607 11.04321918181818 9.17597490909091 4.1281383636363636 4.97340756198347 5.5171746115702485 2.1848901239669414 121.952689897677 84.19851553226592 17.041526349326315 38.41901825757145 44.11913462622769 6.885287929257149 6.1983076930377905 6.6422236206128815 2.623983218173689
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user_005 Jogging 1.4460465343e12 -3.14167 -17.74171 3.21831 0.5684354545454545 -8.31839309090909 -0.5754035454545446 9.8700903889 314.7682737241 10.357519256099998 18.30289275959131 13.293004784553316 3.7101054545454546 9.42331690909091 3.7937135454545445 4.222201925619835 7.810693338842976 4.760586694214876 13.764882483847934 88.79890156915867 14.39226246496529 25.92933548225511 79.23515047717568 32.34629293348333 5.092085572950941 8.901412836015172 5.687380146735695
user_005 Jogging 1.446046535336e12 13.79591 -19.58108 -3.33447 0.8018412727272726 -8.168594818181818 -0.40818800000000005 190.32713272809997 383.4186939664 11.1186901809 24.183972313815612 13.264153394433299 12.994068727272726 11.412485181818182 2.926282 4.401135628099173 7.751153892561984 4.965488429752067 168.84582208908705 130.2448180252196 8.563126343524 30.875727116802615 81.80166573789738 34.38620489012605 5.5565931214011535 9.044427330566451 5.863975178164217
user_005 Jogging 1.446046535466e12 2.60638 11.61165 7.58682 0.7356521818181817 -8.203432090909091 -0.5266325454545453 6.793216704400001 134.8304157225 57.559837712400004 14.113237408167553 13.255970167815521 1.8707278181818183 19.81508209090909 8.113452545454546 4.314676371900827 7.832861909090908 4.815374297520662 3.4996225697193064 392.63747826946616 65.82811220734285 30.481313367488237 83.02335248056642 32.21978126860708 5.520988441165969 9.111715122882542 5.676247111305768
user_005 Jogging 1.446046535855e12 -1.72382 -1.03405 -6.36177 1.2233646363636366 -8.213882727272726 -0.599789818181818 2.9715553923999996 1.0692594024999997 40.4721175329 6.671801280598816 13.037914555049912 2.9471846363636365 7.179832727272726 5.761980181818182 3.9606093884297526 8.004827487603306 4.7821222314049585 8.68589728081786 51.54999799161651 33.20041561566549 27.13730258213853 83.43492617701699 30.17409682118895 5.2093476157901515 9.134272066071658 5.493095377033695
user_005 Jogging 1.446046536437e12 2.49142 -13.67975 6.62882 1.3627123636363636 -7.778423909090909 -0.9481554545454542 6.207173616400001 187.13556006250002 43.9412545924 15.40402506721214 13.505095304889357 1.1287076363636366 5.901326090909091 7.576975454545455 4.147145239669422 7.830643504132232 5.837039223140496 1.2739809283855872 34.825649631244374 57.4105570387843 31.226787615125485 80.20664756182254 42.00361180619343 5.588093379241751 8.955816409564376 6.481019349314846
user_005 Jogging 1.446046536566e12 2.72134 -6.85874 -8.54603 1.4358696363636363 -8.659791181818182 -0.5997890909090908 7.405691395600001 47.0423143876 73.0346287609 11.290820809139609 14.161374394521529 1.2854703636363638 1.801051181818182 7.946240909090909 4.340646545454546 7.698897280991735 5.504824561983471 1.6524340557874053 3.2437853595286703 63.14274458530991 33.926766159153416 82.07243264506836 39.69246186369529 5.824668759608001 9.059383679095856 6.30019538297784
user_005 Jogging 1.446046537191e12 -8.88971 -19.58108 8.58315 -3.7200084545454546 -12.683423636363635 8.053690000000001 79.02694388409998 383.4186939664 73.67046392249999 23.154181086209892 19.006897586499694 5.1697015454545445 6.897656363636365 0.5294599999999985 3.929191355371901 8.388347768595041 4.496189636363636 26.725814069075106 47.57766331081324 0.2803278915999984 37.982441675489866 95.07989014595297 45.417514090548984 6.1629896702404 9.75089176157509 6.739251745598245
user_005 Jogging 1.446046537199e12 -7.39522 -19.58108 2.6435 -2.8212230000000003 -15.661957272727271 6.855309090909091 54.6892788484 383.4186939664 6.98809225 21.097299947263394 18.48057756225118 4.573997 3.919122727272729 4.211809090909091 2.83911620661157 7.010399669421488 3.3991572892561988 20.921448556009004 15.359522951425634 17.73933581826446 14.939538625687815 63.39304411683022 22.938252788811482 3.865169934904262 7.961974887980382 4.789389605034391
user_005 Jogging 1.446046537247e12 2.33814 -11.8787 -8.46939 -3.695568181818182 -17.215671818181818 -4.0451345454545455 5.466898659600001 141.10351369 71.73056697210001 14.775011990577198 20.703948053627844 6.033708181818183 5.3369718181818175 4.424255454545455 4.618996033057852 5.3781446280991725 7.32362917355372 36.40563442333968 28.483268188066937 19.574036327075213 25.153184588790236 36.76646394369556 94.20583036550964 5.015295064977757 6.063535597627474 9.705968800975493
user_005 Jogging 1.446046537506e12 4.25415 -19.58108 -7.12818 11.86596181818182 -19.25013181818181 -3.574839363636364 18.0977922225 383.4186939664 50.81095011240001 21.267990885396298 24.067887578832163 7.6118118181818195 0.3309481818181901 3.5533406363636364 8.285105297520662 6.445729578512396 4.262738148760331 57.93967915541241 0.1095266990487658 12.626229678033132 94.68215108093536 61.12387683692416 22.080502893756435 9.730475377952269 7.818176055636261 4.698989560932907
user_005 Jogging 1.446046537628e12 1.95493 13.60431 7.7401 1.090985181818182 2.644700909090909 4.172831818181819 3.8217513049000003 185.0772505761 59.90914801 15.773653663340019 11.77319875359906 0.8639448181818181 10.95960909090909 3.5672681818181813 3.8969519008264473 13.113463801652891 4.991775173553719 0.7464006488632148 120.11303142553717 12.725402281012393 23.85319022932108 201.51069996120503 25.8405193778445 4.88397279162375 14.195446451633885 5.0833570972187765
user_005 Jogging 1.4460465377e12 -3.14167 -3.90807 -1.38013 0.41863736363636356 5.396795727272727 3.998649181818182 9.8700903889 15.2730111249 1.9047588169000003 5.200755746110366 8.354313194227272 3.5603073636363636 9.304865727272727 5.3787791818181825 1.4473028016528926 7.501913107438015 3.2230250247933885 12.675788523563314 86.58052620257462 28.931265486760676 3.4301140495762428 69.1345025313832 12.806767356329642 1.8520567079806824 8.314716022293437 3.5786544058248544
user_005 Jogging 1.446046537798e12 12.60798 -11.95534 0.229323 7.236171454545453 -15.864010909090911 -2.282398818181818 158.9611596804 142.93015451559998 5.2589038329e-2 17.376533118960438 23.27245020551651 5.371808545454546 3.9086709090909117 2.511721818181818 6.8476180165289255 8.136574719008266 12.404698256198346 28.856327049018486 15.277708275573575 6.308746491930577 72.38351563915937 83.04199427584591 203.43031800479287 8.507850236056072 9.112738023000876 14.262900055907034
user_005 Jogging 1.446046537806e12 9.77228 -10.57581 5.13432 8.497257818181817 -16.17057363636364 -0.5788870000000004 95.4974563984 111.84775715610002 26.361241862399996 15.287460724950368 23.214003915053574 1.2750221818181835 5.594763636363638 5.713207000000001 6.64493258677686 7.828745190082646 11.612955909090909 1.625681564128401 31.301380146776875 32.640734224849005 71.41476358365733 78.55517815891763 187.48812677917655 8.45072562468202 8.863135909987934 13.692630382040427
user_005 Jogging 1.446046537927e12 -3.83143 -18.50811 -14.17911 -4.218119 -18.00646363636363 1.1385608181818176 14.6798558449 342.55013577209996 201.04716039209998 23.62788928383363 20.373295370199216 0.3866889999999996 0.5016463636363682 15.317670818181817 6.313667504132232 4.587668512396696 4.9331842727272734 0.1495283827209997 0.2516490741495913 234.6310392941788 50.65188862554589 26.09155367340835 49.933594930582096 7.11701402454329 5.107989200596292 7.066370704299492
user_005 Jogging 1.446046538089e12 0.805325 -0.650847 -0.728685 -6.789063272727273 -8.649263636363637e-2 -4.107839545454545 0.6485483556249999 0.42360181740899994 0.530981829225 1.2661484913938805 9.135670010436984 7.594388272727273 0.5643543636363636 3.379154545454545 7.67958094214876 3.2204892809917354 3.0206535537190082 57.674733236937534 0.3184958477554049 11.418685442066112 73.21571867055573 14.941258901488242 12.832239867491966 8.556618413284289 3.8653924640957538 3.5822115888780166
user_005 Jogging 1.446046538178e12 15.86521 -19.58108 -6.13185 3.5330351818181813 -11.899599272727274 -0.930738 251.70488834409997 383.4186939664 37.5995844225 25.936907424228508 13.572404537765589 12.332174818181818 7.681480727272726 5.201112 4.570884867768594 7.491462446280992 4.1911655206611576 152.08253574619775 59.00514616346233 27.051566036544003 38.07839845566661 76.72006506801198 21.170354081173457 6.1707696809771315 8.758999090536086 4.601125305963038
user_005 Jogging 1.446046538493e12 9.77228 -12.83671 11.61046 1.1467243636363635 -8.997707272727272 -2.7074071818181817 95.4974563984 164.7811236241 134.8027814116 19.876653677973565 13.231876040647904 8.625555636363636 3.839002727272728 14.317867181818182 2.7254921900826443 6.384607595041322 8.92989958677686 74.40021003600448 14.737941940007444 205.0013206361861 13.09131786918851 45.14691348141067 102.19151263494622 3.618192624666148 6.719145293964901 10.108981780325168
user_005 Jogging 1.44604653851e12 19.54396 -19.58108 -17.24474 4.961337090909091 -11.714966363636364 -3.1637672727272728 381.96637248159993 383.4186939664 297.38105766760003 32.60009392801806 17.782204210454342 14.582622909090908 7.866113636363636 14.080972727272727 4.728282619834711 6.480883942148759 10.929839975206612 212.652890908743 61.875743740185946 198.2737929461983 47.499936104067004 46.55667068685511 135.73274442981278 6.892019740545365 6.823244879590289 11.650439666802828
user_005 Jogging 1.446046538793e12 -0.574206 -3.98471 -7.28146 -7.8376469090909096 -0.5324014545454545 -6.713621181818181 0.329712530436 15.877913784100002 53.0196597316 8.320293627398975 12.435762186053363 7.263440909090909 3.452308545454546 0.5678388181818192 7.900635925619834 5.027245347107438 2.382826198347108 52.757573839855375 11.918434293018482 0.32244092343412517 85.47902965290235 37.76294123158168 10.598142654253946 9.245486988412365 6.145155915970048 3.2554788671183146
user_005 Jogging 1.446046538826e12 -7.6042e-2 -3.48655 -0.1922 -5.848474090909092 -1.5147946363636364 -3.268276545454546 5.782385764e-3 12.1560309025 3.694084e-2 3.4926714887409607 8.79684486571532 5.772432090909092 1.9717553636363634 3.076076545454546 7.780923876033058 2.39739494214876 3.527368603305786 33.32097224415711 3.8878192140287675 9.462246913495573 76.2985903174133 7.323591190988912 15.880524485696595 8.73490642865814 2.706213441506215 3.9850375764472528
user_005 Jogging 1.446046538939e12 0.11556 -19.58108 -11.68829 10.354050363636363 -19.23271363636363 -4.720963272727273 1.3354113599999998e-2 383.4186939664 136.6161231241 22.804564701043954 23.674808329678697 10.238490363636362 0.3483663636363694 6.967326727272727 8.065950421487605 6.036874181818183 4.233919008264463 104.82668492627465 0.12135912331322717 48.54364172456889 87.57518667666108 52.2563347149799 22.62891425410126 9.358161500885796 7.228854315517771 4.756985837071754
user_005 Jogging 1.446046538947e12 -3.94639 -19.58108 -8.85259 10.044004545454545 -19.570629090909087 -5.835736 15.5739940321 383.4186939664 78.36834970809998 21.84859349492777 24.18511751724803 13.990394545454546 1.0450909090913285e-2 3.0168539999999995 9.269081396694215 5.096284652892563 4.0549853140495875 195.7311395374843 1.0922150082653395e-4 9.101408057315997 105.31697516413934 42.50487940249286 21.1970906556682 10.26240591499573 6.519576627549742 4.604029827843017
user_005 Jogging 1.446046538979e12 -4.9044 -13.48815 4.48288 3.7316036363636367 -18.936601818181813 -4.727930727272727 24.05313936 181.93019042249998 20.0962130944 15.03594170236437 22.799217118887203 8.636003636363636 5.448451818181814 9.210810727272726 10.874417636363638 2.1022333057851252 4.469224636363635 74.58055880728594 29.68562721504872 84.83903425364232 137.5093735084357 9.196215785575577 26.529507394367275 11.726439080489682 3.0325263041852706 5.150680284619428
user_005 Jogging 1.446046539076e12 2.22318 4.714 7.58682 3.337951181818182 8.69234272727273 7.287228181818182 4.9425293124000005 22.221796000000005 57.559837712400004 9.204572940924528 12.255265287128658 1.114771181818182 3.9783427272727288 0.2995918181818187 3.6958518016528927 12.376827272727269 4.278889537190082 1.2427147878123062 15.827210855643813 8.97552575214879e-2 22.984673684992117 209.9559773255614 26.829853647783384 4.794233378235995 14.489857740004261 5.179754207275031
user_005 Jogging 1.446046539133e12 -1.83878 -5.82409 -7.7413 -0.1352640909090908 1.7459141818181818 1.9432845454545458 3.3811118884000004 33.9200243281 59.927725689999995 9.860469659529407 6.6261052838034376 1.7035159090909093 7.570004181818182 9.684584545454545 2.386311570247934 5.564680247933885 4.438188 2.9019664525258273 57.30496331274476 93.79117781805701 7.486160788873022 35.40458672840595 28.815742980033075 2.7360849381685908 5.950175352744316 5.36802971117272
user_005 Jogging 1.446046539158e12 1.91661 -15.67241 -16.55497 -0.5393703636363636 -3.3263021818181815 -4.480592727272727 3.6733938920999996 245.62443520809998 274.06703170090003 22.877168985718054 9.004548610586447 2.4559803636363635 12.346107818181817 12.074377272727274 2.4233651074380167 7.4813292396694235 7.8037251239669425 6.031839546567404 152.4263782581702 145.79058652415293 7.831012942022457 59.9454553949351 78.68714381250022 2.7983947080464646 7.742445052755305 8.870577422721714
user_005 Jogging 1.446046539262e12 -3.29495 -8.96635 8.08499 7.434739363636364 -11.014747272727275 7.938672727272728 10.856695502500001 80.3954323225 65.36706330009999 12.514758931961094 18.097212429523772 10.729689363636364 2.048397272727275 0.14631727272727169 8.480824768595042 2.806567272727272 8.609085867768597 115.12623384013132 4.195931386916539 2.1408744298346803e-2 87.08888798453219 11.310359394584937 97.52241800503252 9.332142732756084 3.363087776818342 9.875343943632167
user_005 Jogging 1.446046539302e12 -5.90073 -19.58108 9.00468 0.3803184545454543 -14.035085454545454 8.408968181818182 34.8186145329 383.4186939664 81.0842619024 22.345504478567943 17.498293291626553 6.281048454545455 5.545994545454546 0.5957118181818188 7.303660975206612 3.1999061157024795 3.8785865289256205 39.451569688347845 30.758055498211576 0.3548725703214884 61.10605286841874 15.428117018312696 27.387089683350485 7.8170360667211165 3.927864180227302 5.233267591414611
user_005 Jogging 1.446046539319e12 -12.76007 -19.58108 -0.996927 -3.8209815454545453 -14.57853727272727 6.8204166363636345 162.81938640490003 383.4186939664 0.993863443329 23.39298920220819 17.550602729410397 8.939088454545455 5.002542727272729 7.817343636363635 8.1581096446281 3.2246087603305784 3.2974476859504134 79.90730239818785 25.025433738189275 61.11086152899502 70.00862498085486 15.035771101271676 18.016229528635986 8.367115690657974 3.877598625602149 4.244552924471079
user_005 Jogging 1.4460465394e12 7.39642 -2.56686 -6.85994 2.146536363636363 -14.540217272727268 -8.664473363636363 54.7070288164 6.5887702596 47.0587768036 10.409350406226125 20.08056548210617 5.249883636363637 11.973357272727268 1.804533363636363 8.138792611570247 5.077282975206612 7.848378743801652 27.561278195358685 143.36128438037096 3.256340660476766 80.77637375669282 37.16680859849946 89.7226633472793 8.987567733079558 6.0964586932496685 9.472204777520348
user_005 Jogging 1.446046539578e12 7.20482 -19.58108 -5.59536 0.6590119999999999 -9.952231818181817 -0.3907689090909091 51.909431232399996 383.4186939664 31.308053529600002 21.601763324515893 10.362929003394015 6.545808 9.628848181818183 5.2045910909090916 4.776739033057851 5.110536950413223 4.43185461983471 42.847602372864 92.71471730850334 27.08776842357029 36.474788326173105 42.3693493244356 21.37286011656183 6.039436093392586 6.509174242900216 4.623079073146147
user_005 Jogging 1.44604653961e12 19.16076 -19.58108 1.83878 6.097012454545455 -15.902331818181814 -1.007377 367.1347237776 383.4186939664 3.3811118884000004 27.457868264532117 18.36803215234251 13.063747545454545 3.678748181818186 2.846157 5.852874611570247 6.96764694214876 3.697434991735537 170.66149993136963 13.533188185230609 8.100609668649 58.13333525565159 55.72582041356123 16.12637407479173 7.624521968992652 7.464972901060072 4.0157656897273935
user_005 Jogging 1.446046539682e12 -6.89706 -9.50284 5.67081 3.9998454545454547 -18.448889090909088 -3.1358959090909093 47.5694366436 90.30396806560002 32.158086056100004 13.03961237020871 22.043440536798908 10.896905454545454 8.946049090909087 8.80670590909091 10.263827082644628 2.2273277685950434 3.8956880661157025 118.74254848530246 80.0317943369553 77.55806896921675 120.76651362675165 12.032200956290906 21.95008966866136 10.989381858264442 3.468746309012942 4.685092279631358
user_005 Jogging 1.446046539755e12 0.345482 6.70665 10.88237 0.10510900000000002 6.06217509090909 8.36019909090909 0.119357812324 44.9791542225 118.4259768169 12.78766940656991 14.882968130300673 0.240373 0.6444749090909099 2.52217090909091 4.839443595041322 13.605293487603307 7.101292727272729 5.7779179129e-2 0.41534790844773656 6.361346094664468 39.33490163750689 251.6198299976049 54.91098830766759 6.27175427113554 15.862529117313068 7.4101948899922725
user_005 Jogging 1.446046539772e12 1.87829 3.87095 8.73643 1.6692744545454545 9.27411418181818 9.293819999999998 3.5279733241 14.9842539025 76.3252091449 9.738451436008704 13.889704399334034 0.20901554545454548 5.403164181818179 0.557389999999998 2.7011064214876033 13.387405983471075 5.818670082644629 4.368749824166117e-2 29.19418317568291 0.31068361209999784 12.831011815806407 247.56773383231638 43.55359550083381 3.5820401750687285 15.734285297792091 6.599514792833926
user_005 Jogging 1.446046539942e12 0.537083 -9.27292 11.76374 6.584724818181818 -9.77108 4.778988181818182 0.28845814888899995 85.98704532639998 138.3855787876 14.988698484621304 16.5450927999781 6.047641818181818 0.4981600000000004 6.9847518181818185 4.964222173553718 3.317082661157025 9.577860421487607 36.57397156102149 0.24816338560000037 48.78675796159422 37.43595558677263 25.67015866625859 127.0524021856521 6.118492917931068 5.066572674526498 11.271752400831563
user_005 Jogging 1.44604653999e12 -0.804128 -19.58108 5.40257 3.156799727272728 -10.986879090909092 7.015502727272727 0.646621840384 383.4186939664 29.187762604899998 20.32862706657004 15.52897945485492 3.960927727272728 8.594200909090908 1.6129327272727272 5.840839694214875 2.2605820661157026 4.385301074380165 15.6889484606779 73.86028926581899 2.601551982707438 40.40700436750239 12.320737220128098 25.776883221690685 6.356650404694472 3.5100907709243216 5.077093974085046
user_005 Jogging 1.446046540096e12 9.8106 0.613724 -5.25048 2.376456363636364 -13.192039636363639 -8.350943636363636 96.24787236000002 0.37665714817600005 27.567540230399995 11.14414957448867 18.601696635532743 7.434143636363637 13.805763636363638 3.100463636363637 6.501151743801654 6.114781735537192 7.790107867768596 55.266491606085964 190.59910958314055 9.612874760413225 54.78844817181653 52.86952324153863 86.24638087968755 7.401921924190806 7.271143186703081 9.286892961571569
user_005 Jogging 1.446046540104e12 2.2615 1.95493 -8.66099 3.400654545454545 -11.234220545454544 -8.657506363636365 5.114382249999999 3.8217513049000003 75.0127477801 9.16236221369795 17.417205621653796 1.139154545454545 13.189150545454545 3.483636363634801e-3 5.963083008264463 6.803280214876033 6.720622851239669 1.2976730784297512 173.95369211066392 1.21357223140387e-5 50.3778636743197 65.81661171360078 73.65714927952101 7.097736517673765 8.112743784540516 8.582374338114192
user_005 Jogging 1.44604654012e12 -13.06663 -2.2603 -14.94552 2.752692727272727 -7.8515822727272715 -9.939495454545453 170.7368195569 5.1089560899999995 223.36856807040002 19.98034893882737 16.54993111786699 15.819322727272727 5.5912822727272715 5.006024545454547 7.762237380165288 7.418938900826446 5.458586206611571 250.25097154960744 31.26243745331424 25.060281749693406 79.2542529639753 73.90660281971599 53.25524326196705 8.902485774432627 8.59689495223223 7.297619013210203
user_005 Jogging 1.446046540161e12 -9.69444 -3.14167 -4.9056 -5.496624545454545 -2.319522272727273 -7.13166090909091 93.9821669136 9.8700903889 24.064911359999996 11.310047244043679 15.320231174103524 4.197815454545455 0.8221477272727271 2.2260609090909105 11.350412371900823 6.493867867768595 3.1625339338842977 17.621654590420665 0.6759268854597105 4.955347170982651 159.6364509893014 66.65468024152023 12.332436510854023 12.63473193183383 8.164231760644734 3.5117568980289655
user_005 Jogging 1.446046540193e12 1.41845 -3.52487 -0.307161 -9.380910363636366 -3.1695362727272727 -7.542732818181817 2.0120004025 12.424708516899999 9.434787992100001e-2 3.8119623292106386 14.2613084737019 10.799360363636366 0.3553337272727273 7.235571818181818 10.904820504132232 2.8220859338842974 3.948575702479339 116.62618426368017 0.12626205773752894 52.353499536066934 151.38493928892447 15.014976780614317 17.83407046135147 12.303858715416252 3.8749163578862342 4.22304042857175
user_005 Jogging 1.446046540217e12 -2.29862 -6.7821 0.689167 -6.287415909090908 -4.050903636363636 -3.8430809090909097 5.2836539044 45.996880409999996 0.47495115388899994 7.1941285412681495 10.53827068016974 3.9887959090909075 2.7311963636363634 4.53224790909091 8.581849818181821 1.5055775371900824 4.445789826446281 15.91049280438036 7.459433576740495 20.541271109458926 97.87125545609757 3.4811748435715795 22.0431335507613 9.892990218134129 1.865790675175428 4.695011560237238
user_005 Jogging 1.446046540339e12 -2.10702 -19.58108 -9.65732 9.967363636363636 -19.52882545454545 -3.710701727272727 4.439533280399999 383.4186939664 93.2638295824 21.934494679139522 23.708771637632957 12.074383636363637 5.225454545454866e-2 5.946618272727273 9.42869852892562 4.468590330578514 4.145560669421488 145.79074019808596 2.730537520661492e-3 35.36226888153389 110.2410839227691 32.07802959815651 22.283775548103858 10.499575416309419 5.6637469574616865 4.720569409308993
user_005 Jogging 1.446046540514e12 5.13552 -2.79678 -7.89458 -2.3648110000000004 -7.228005272727272 -7.724018181818183e-2 26.373565670399998 7.8219783684 62.3243933764 9.824456087499195 16.574582047151853 7.500331 4.431225272727272 7.817339818181819 9.026175991735538 8.765533487603308 6.827665371900826 56.254965109561 19.63575741765689 61.11080183293095 104.91049056532684 167.91245901524488 57.88847597379886 10.2425822215556 12.958103989984217 7.608447671752685
user_005 Jogging 1.446046540563e12 4.33079 -10.57581 1.14901 1.3104566363636363 -4.935754363636364 -4.727931818181819 18.7557420241 111.84775715610002 1.3202239801000002 11.485805290022116 16.556757493226794 3.020333363636364 5.640055636363637 5.87694181818182 3.7015521404958673 12.720126892561984 11.229750066115702 9.122413627494954 31.81022758127723 34.53844513429423 17.429640415905563 216.0190225727229 139.08506675730447 4.174882084072023 14.697585603517432 11.793433204851947
user_005 Jogging 1.446046540717e12 -6.51385 -19.58108 -6.43841 -2.0268926363636366 -14.97219181818182 4.50029790909091 42.430241822499994 383.4186939664 41.453123328100006 21.61717046972152 17.517867329058955 4.486957363636363 4.60888818181818 10.93870790909091 5.2619166611570245 3.4266593388429754 4.726067801652892 20.132786383090583 21.241850272503292 119.65533072040803 35.40847356546848 18.10052390631796 32.93065278676701 5.950501959118111 4.254471048945798 5.738523572032009
user_005 Jogging 1.446046540725e12 -2.2603 -19.58108 -13.68095 -1.9711544545454545 -15.864009999999997 2.100052454545455 5.1089560899999995 383.4186939664 187.1683929025 23.993666726011263 18.21761657089616 0.2891455454545455 3.717070000000003 15.781002454545455 4.390684289256199 3.647080165289256 5.649555338842974 8.360514645620665e-2 13.816609384900024 249.04003847036967 26.55514334235929 19.20472444099144 52.69664942424522 5.153168281975594 4.382319527486722 7.259245788940144
user_005 Jogging 1.446046540822e12 -17.85667 -2.6435 -5.71033 -1.9746390909090907 -4.9949745454545456 -9.228827272727273 318.86066348890006 6.98809225 32.6078687089 18.932950759134194 15.92906364072432 15.882030909090911 2.3514745454545456 3.5184972727272728 9.308036595041322 7.645694710743802 3.4605465619834708 252.2389057973191 5.529432537920662 12.379823058189256 111.33812321837313 84.26482645558666 22.85573815537694 10.551688169121238 9.179587488312677 4.780767527853341
user_005 Jogging 1.44604654083e12 -14.75272 -3.21831 -3.14286 -3.5666736363636358 -3.8558163636363645 -8.222047272727272 217.6427473984 10.357519256099998 9.877568979600001 15.42328874248615 15.386100335157364 11.186046363636365 0.6375063636363647 5.079187272727271 9.959798661157025 7.569370495867769 2.874974024793388 125.12763324942235 0.40641436367686085 25.798143351434696 121.24667289853097 84.10343286667974 13.135425839644437 11.011206695840878 9.170792379433728 3.6242828034860133
user_005 Jogging 1.446046540838e12 -10.72909 -3.25663 -3.2195 -4.94968909090909 -2.831619090909091 -7.389450909090908 115.11337222809999 10.6056389569 10.36518025 11.66551290921235 14.664609256904741 5.779400909090909 0.4250109090909091 4.169950909090908 9.997485338842976 7.3236142148760335 2.544659586776859 33.401474868000825 0.180634272846281 17.388490584228094 121.66666259466352 83.23017701976578 9.180451949874753 11.030261220599607 9.123057438148999 3.029926063433686
user_005 Jogging 1.446046540927e12 -4.40624 -6.24561 0.497565 -2.3682936363636364 -2.302102909090909 -3.285694818181818 19.414950937600004 39.0076442721 0.24757092922499999 7.659645301117083 5.719106541657371 2.037946363636364 3.9435070909090912 3.783259818181818 4.485693983471075 1.3127083719008263 3.0485239504132235 4.153225381058679 15.551248176050283 14.313054851869122 31.307420746990218 2.6778831208879526 12.53341286799084 5.595303454415159 1.6364238817885641 3.540256045541175
user_005 Jogging 1.446046540976e12 3.2195 -19.58108 -6.9749 -3.1137981818181815 -10.206538636363636 -1.711078363636364 10.36518025 383.4186939664 48.64923001 21.034093853227905 11.824510576150509 6.333298181818181 9.374541363636364 5.263821636363636 2.541175404958677 6.296882462809918 2.6064149173553717 40.11066585982148 87.88202577852914 27.707818219449944 9.363454819684579 59.75930482568696 9.126199517026393 3.0599762776342856 7.730414272578602 3.020960032345081
user_005 Jogging 1.446046541161e12 3.33447 3.52607 4.7128 1.1502080909090908 9.664284545454546 10.102029090909092 11.1186901809 12.4331696449 22.21048384 6.764787037727056 14.376779236094603 2.1842619090909094 6.138214545454546 5.389229090909092 3.1340315041322313 12.022759669421486 6.602495041322314 4.771000087505464 37.677677806029756 29.04379019430084 12.984159483889442 206.43890998226743 57.00039092718214 3.60335392154163 14.367982112400734 7.549860325011459
user_005 Jogging 1.446046541235e12 7.58802 -19.58108 -19.54396 2.4949023636363634 -3.928976181818182 -3.397172818181819 57.578047520400006 383.4186939664 381.96637248159993 28.687333685241644 9.474860604030479 5.093117636363637 15.652103818181818 16.14678718181818 2.017675578512397 8.562214818181818 8.995139520661157 25.93984725783832 244.98835393514184 260.71873629492785 5.3878930097540945 83.3646869357908 98.37953343385551 2.3211835364214726 9.130426437784317 9.918645745960257
user_005 Jogging 1.44604654134e12 -1.57053 -7.85507 11.4955 3.2404081818181822 -8.774752727272727 9.586448181818183 2.4665644809 61.70212470490001 132.14652025 14.011252957383933 15.148865444150692 4.810938181818182 0.9196827272727264 1.9090518181818172 4.711814024793388 2.3742772479338843 9.278583223140494 23.145126189276034 0.8458163188438 3.6444788445033023 27.561006826288562 7.091636321663279 126.34631874555262 5.249857791053826 2.66301264016213 11.240387837861851
user_005 Jogging 1.446046541412e12 6.59169 -19.58108 -15.52033 -1.9885736363636364 -16.68963909090909 -0.8122936363636359 43.450377056099995 383.4186939664 240.88064330889998 25.840853591385095 21.518287655835156 8.580263636363636 2.8914409090909103 14.708036363636364 5.809802975206612 4.999057190082644 9.224111239669421 73.62092406950413 8.36043053076447 216.32633367404958 39.01585487781022 30.637290880641924 151.2366587860819 6.246267275566281 5.535096284676711 12.297831466810802
user_005 Jogging 1.446046541517e12 -9.6178 -1.57053 -5.4804 -3.333268181818182 -1.7725854545454547 -7.323260909090909 92.50207684000002 2.4665644809 30.034784160000005 11.180493078612411 16.414639162431733 6.284531818181819 0.2020554545454547 1.8428609090909083 12.730577107438016 7.694465123966942 2.576645785123967 39.49534017373968 4.082640671157031e-2 3.396136330255369 192.85396690384394 111.32270980228442 8.473371684080687 13.887187148729721 10.550957767060032 2.9109056467155865
user_005 Jogging 1.446046541526e12 -5.24928 -1.37893 -9.619 -4.914851818181818 -0.8563818181818182 -7.8109745454545445 27.5549405184 1.9014479449 92.525161 11.044525769054097 15.8521414573526 0.3344281818181818 0.5225481818181817 1.8080254545454553 11.748183140495867 7.11649305785124 2.5883634710743793 0.11184220879421486 0.27305660232148754 3.2689560442843 181.58080947832903 107.04410449639293 8.514233087209762 13.475192372590792 10.34621208444873 2.9179158807631453
user_005 Jogging 1.446046541542e12 0.307161 -2.68182 -3.87095 -7.788874454545455 -1.243068181818182 -8.194178181818181 9.434787992100001e-2 7.192158512400001 14.9842539025 4.719190639804775 14.113925983821156 8.096035454545456 1.4387518181818182 4.32322818181818 10.823112314049588 4.726066363636364 2.2985858677685944 65.54579008125705 2.0700067943214875 18.69030191206693 164.5818232479703 64.88748743124589 7.553243462068892 12.828944744131151 8.055276992831836 2.74831647778579
user_005 Jogging 1.446046541567e12 -3.67815 -1.53221 -1.64837 -7.945640363636364 -2.6504690909090916 -5.546593272727272 13.5287874225 2.3476674841 2.7171236568999997 4.312027198835833 10.93577854426604 4.267490363636364 1.1182590909090915 3.8982232727272725 10.032953694214877 1.1673442975206612 3.1954715867768595 18.211474003729226 1.2505033944008277 15.196144684032527 144.1504480278062 1.9028610728867017 14.167965256505674 12.006267031338517 1.3794423050228313 3.7640357671660976
user_005 Jogging 1.44604654159e12 -7.3569 -7.81675 3.94639 -4.799891272727273 -2.9047763636363633 -2.5401904545454546 54.123977610000004 61.1015805625 15.5739940321 11.436763187397036 7.609283436074653 2.557008727272727 4.911973636363637 6.486580454545455 5.092799677685949 1.3836494214876036 4.091723454545454 6.538293631348892 24.12748500433141 42.075725993291115 37.86155491294937 3.7278022676234417 20.641978826787177 6.153174376933371 1.9307517364030626 4.543344453900362
user_005 Jogging 1.446046541647e12 12.68462 -19.58108 -8.23947 -3.9045899999999993 -12.63116909090909 1.8352919090909092 160.89958454440003 383.4186939664 67.88886588090001 24.742820057376242 15.833626551545684 16.58921 6.94991090909091 10.07476190909091 5.423432454545455 6.832734214876033 5.923814867768595 275.20188842410005 48.301261644300844 101.50082752486911 49.805850736926025 62.230873282694525 41.61672815250327 7.057326033061391 7.888654719449605 6.451102863270998
user_005 Jogging 1.446046541704e12 -0.804128 -19.58108 -2.03158 8.35791109090909 -19.581079999999996 -0.5022472727272728 0.646621840384 383.4186939664 4.127317296399999 19.70260472889775 23.37056805963689 9.16203909090909 3.552713678800501e-15 1.529332727272727 10.50261695041322 4.642774710743804 4.055621512396694 83.94296030334627 1.2621774483536189e-29 2.3388585907074373 146.0293819989988 37.699085315443725 26.298503606760573 12.084261748199548 6.1399580874338 5.128206665761489
user_005 Jogging 1.446046541777e12 2.4531 19.54396 15.94065 -1.5252460909090912 -3.827948181818181 6.688037636363637 6.01769961 381.96637248159993 254.1043224225 25.33946318519988 18.518431558431583 3.978346090909091 23.371908181818178 9.252612363636363 7.945605561983471 11.386833388429755 5.833873041322314 15.827237619051646 546.2460920593395 85.61083555171648 88.88585335568426 235.8254541440598 43.61219456277871 9.42792943098771 15.356609461207894 6.603952949770214
  1. Prediction using Random Forests

Instead of just stopping at ETL and feature engineering let's quickly see without understanding the random forest model in detail how simple it is to predict the activity using random forest model.

val splits = dataFeatDF.randomSplit(Array(0.7, 0.3))
val (trainingData, testData) = (splits(0), splits(1))
splits: Array[org.apache.spark.sql.Dataset[org.apache.spark.sql.Row]] = Array([user_id: string, activity: string ... 27 more fields], [user_id: string, activity: string ... 27 more fields])
trainingData: org.apache.spark.sql.Dataset[org.apache.spark.sql.Row] = [user_id: string, activity: string ... 27 more fields]
testData: org.apache.spark.sql.Dataset[org.apache.spark.sql.Row] = [user_id: string, activity: string ... 27 more fields]
import org.apache.spark.ml.feature.{StringIndexer,VectorAssembler}
import org.apache.spark.ml.Pipeline

import org.apache.spark.ml.classification.RandomForestClassifier

val transformers = Array(
              new StringIndexer().setInputCol("activity").setOutputCol("label"),
              new VectorAssembler()
                      .setInputCols(Array("meanX", "meanY", "meanZ", "stddevX", "stddevY","stddevZ"))
                      .setOutputCol("features")
)

// Train a RandomForest model.
val rf = new RandomForestClassifier() 
              .setLabelCol("label")
              .setFeaturesCol("features")
              .setNumTrees(10)
              .setFeatureSubsetStrategy("auto")
              .setImpurity("gini")
              .setMaxDepth(20)
              .setMaxBins(32)
              .setSeed(12345)

val model = new Pipeline().setStages(transformers :+ rf).fit(trainingData)
import org.apache.spark.ml.feature.{StringIndexer, VectorAssembler}
import org.apache.spark.ml.Pipeline
import org.apache.spark.ml.classification.RandomForestClassifier
transformers: Array[org.apache.spark.ml.PipelineStage with org.apache.spark.ml.param.shared.HasOutputCol with org.apache.spark.ml.param.shared.HasInputCols with org.apache.spark.ml.param.shared.HasHandleInvalid with org.apache.spark.ml.util.DefaultParamsWritable{def copy(extra: org.apache.spark.ml.param.ParamMap): org.apache.spark.ml.PipelineStage with org.apache.spark.ml.param.shared.HasOutputCol with org.apache.spark.ml.param.shared.HasInputCols with org.apache.spark.ml.param.shared.HasHandleInvalid with org.apache.spark.ml.util.DefaultParamsWritable{def copy(extra: org.apache.spark.ml.param.ParamMap): org.apache.spark.ml.PipelineStage with org.apache.spark.ml.param.shared.HasOutputCol with org.apache.spark.ml.param.shared.HasInputCols with org.apache.spark.ml.param.shared.HasHandleInvalid with org.apache.spark.ml.util.DefaultParamsWritable}}] = Array(strIdx_84996728c97a, VectorAssembler: uid=vecAssembler_e11ceeee69a9, handleInvalid=error, numInputCols=6)
rf: org.apache.spark.ml.classification.RandomForestClassifier = rfc_6ab6b8d21734
model: org.apache.spark.ml.PipelineModel = pipeline_dd3e9eb4d47c

Before we go further let's find quickly which label is mapped to which activity by the StringIndexer and quickly check that the estimator we have built can transform the union of the training and test data. This is mostly for debugging... not something you would do in a real pipeline except during debugging stages.

val activityLabelDF = model.transform(trainingData.union(testData)).select("activity","label").distinct
display(activityLabelDF) // this just shows what activity is associated with what label
activity label
Jogging 0.0
Jumping 4.0
Standing 1.0
Walking 2.0
Sitting 3.0
val myPredictionsOnTestData = model.transform(testData)
display(myPredictionsOnTestData)

Let's evaluate accuracy at a lower level...

val accuracy: Double = 1.0 * model.transform(testData)
                                  .select("activity","label","prediction")
                                  .filter($"label"===$"prediction").count() / testData.count() 
accuracy: Double = 0.9828725226327379

We get 98% correct predictions and here are the mis-predicted ones.

display(model.transform(testData).select("activity","label","prediction").filter(not($"label"===$"prediction")))
activity label prediction
Jogging 0.0 4.0
Jogging 0.0 4.0
Jogging 0.0 4.0
Jogging 0.0 4.0
Jogging 0.0 4.0
Jogging 0.0 4.0
Jumping 4.0 0.0
Jumping 4.0 0.0
Jumping 4.0 0.0
Jumping 4.0 0.0
Jumping 4.0 0.0
Jumping 4.0 0.0
Walking 2.0 1.0
Walking 2.0 1.0
Walking 2.0 1.0
Jogging 0.0 2.0
Standing 1.0 2.0
Standing 1.0 2.0
Standing 1.0 2.0
Standing 1.0 2.0
Standing 1.0 2.0
Jumping 4.0 2.0
Walking 2.0 1.0
Jogging 0.0 4.0
Jogging 0.0 4.0
Jumping 4.0 2.0
Jumping 4.0 0.0
Jumping 4.0 0.0
Jumping 4.0 0.0
Jumping 4.0 0.0
Jumping 4.0 0.0
Jumping 4.0 0.0
Jumping 4.0 0.0
Walking 2.0 0.0
Walking 2.0 0.0
Walking 2.0 0.0
Walking 2.0 0.0
Walking 2.0 0.0
Walking 2.0 0.0
Walking 2.0 0.0
Walking 2.0 0.0
Walking 2.0 0.0
Walking 2.0 0.0
Walking 2.0 0.0
Walking 2.0 0.0
Walking 2.0 0.0
Walking 2.0 0.0
Walking 2.0 0.0
Walking 2.0 0.0
Walking 2.0 0.0
Walking 2.0 0.0
Walking 2.0 0.0
Jogging 0.0 2.0
Jogging 0.0 2.0
Jogging 0.0 4.0
Jogging 0.0 4.0
Jogging 0.0 2.0
Jogging 0.0 4.0
Jogging 0.0 4.0
Jogging 0.0 4.0
Jumping 4.0 2.0
Jumping 4.0 0.0
Jumping 4.0 0.0
Walking 2.0 0.0
Walking 2.0 1.0
Walking 2.0 0.0
Walking 2.0 0.0
Walking 2.0 0.0
Walking 2.0 0.0
Walking 2.0 0.0
testData.printSchema()
root
 |-- user_id: string (nullable = true)
 |-- activity: string (nullable = true)
 |-- timeStampAsLong: long (nullable = true)
 |-- x: double (nullable = true)
 |-- y: double (nullable = true)
 |-- z: double (nullable = true)
 |-- meanX: double (nullable = true)
 |-- meanY: double (nullable = true)
 |-- meanZ: double (nullable = true)
 |-- SqX: double (nullable = true)
 |-- SqY: double (nullable = true)
 |-- SqZ: double (nullable = true)
 |-- resultant: double (nullable = true)
 |-- meanResultant: double (nullable = true)
 |-- absDevFromMeanX: double (nullable = true)
 |-- absDevFromMeanY: double (nullable = true)
 |-- absDevFromMeanZ: double (nullable = true)
 |-- meanAbsDevFromMeanX: double (nullable = true)
 |-- meanAbsDevFromMeanY: double (nullable = true)
 |-- meanAbsDevFromMeanZ: double (nullable = true)
 |-- sqrDevFromMeanX: double (nullable = true)
 |-- sqrDevFromMeanY: double (nullable = true)
 |-- sqrDevFromMeanZ: double (nullable = true)
 |-- varianceX: double (nullable = true)
 |-- varianceY: double (nullable = true)
 |-- varianceZ: double (nullable = true)
 |-- stddevX: double (nullable = true)
 |-- stddevY: double (nullable = true)
 |-- stddevZ: double (nullable = true)

Let's understand the mis-predicitons better by seeing the user_id also.

display(model.transform(testData).select("user_id","activity","label","prediction").filter(not($"label"===$"prediction")))
user_id activity label prediction
user_001 Jogging 0.0 4.0
user_001 Jogging 0.0 4.0
user_001 Jogging 0.0 4.0
user_001 Jogging 0.0 4.0
user_001 Jogging 0.0 4.0
user_001 Jogging 0.0 4.0
user_001 Jumping 4.0 0.0
user_001 Jumping 4.0 0.0
user_001 Jumping 4.0 0.0
user_001 Jumping 4.0 0.0
user_001 Jumping 4.0 0.0
user_001 Jumping 4.0 0.0
user_001 Walking 2.0 1.0
user_001 Walking 2.0 1.0
user_001 Walking 2.0 1.0
user_002 Jogging 0.0 2.0
user_002 Standing 1.0 2.0
user_002 Standing 1.0 2.0
user_002 Standing 1.0 2.0
user_002 Standing 1.0 2.0
user_002 Standing 1.0 2.0
user_003 Jumping 4.0 2.0
user_003 Walking 2.0 1.0
user_004 Jogging 0.0 4.0
user_004 Jogging 0.0 4.0
user_004 Jumping 4.0 2.0
user_004 Jumping 4.0 0.0
user_004 Jumping 4.0 0.0
user_004 Jumping 4.0 0.0
user_004 Jumping 4.0 0.0
user_004 Jumping 4.0 0.0
user_004 Jumping 4.0 0.0
user_004 Jumping 4.0 0.0
user_004 Walking 2.0 0.0
user_004 Walking 2.0 0.0
user_004 Walking 2.0 0.0
user_004 Walking 2.0 0.0
user_004 Walking 2.0 0.0
user_004 Walking 2.0 0.0
user_004 Walking 2.0 0.0
user_004 Walking 2.0 0.0
user_004 Walking 2.0 0.0
user_004 Walking 2.0 0.0
user_004 Walking 2.0 0.0
user_004 Walking 2.0 0.0
user_004 Walking 2.0 0.0
user_004 Walking 2.0 0.0
user_004 Walking 2.0 0.0
user_004 Walking 2.0 0.0
user_004 Walking 2.0 0.0
user_004 Walking 2.0 0.0
user_004 Walking 2.0 0.0
user_005 Jogging 0.0 2.0
user_005 Jogging 0.0 2.0
user_005 Jogging 0.0 4.0
user_005 Jogging 0.0 4.0
user_005 Jogging 0.0 2.0
user_005 Jogging 0.0 4.0
user_005 Jogging 0.0 4.0
user_005 Jogging 0.0 4.0
user_005 Jumping 4.0 2.0
user_005 Jumping 4.0 0.0
user_005 Jumping 4.0 0.0
user_005 Walking 2.0 0.0
user_006 Walking 2.0 1.0
user_006 Walking 2.0 0.0
user_006 Walking 2.0 0.0
user_006 Walking 2.0 0.0
user_006 Walking 2.0 0.0
user_006 Walking 2.0 0.0

Let's evaluate our model's accuracy using ML pipeline's evaluation.MulticlassClassificationEvaluator:

import org.apache.spark.ml.evaluation.MulticlassClassificationEvaluator

// Select (prediction, true label) and compute test error.
val evaluator = new MulticlassClassificationEvaluator()
  .setLabelCol("label")
  .setPredictionCol("prediction")
  .setMetricName("accuracy")
val accuracy = evaluator.evaluate(myPredictionsOnTestData)
println(s"Test Error = ${(1.0 - accuracy)}")
Test Error = 0.017127477367262056
import org.apache.spark.ml.evaluation.MulticlassClassificationEvaluator
evaluator: org.apache.spark.ml.evaluation.MulticlassClassificationEvaluator = MulticlassClassificationEvaluator: uid=mcEval_0923535d6e49, metricName=accuracy, metricLabel=0.0, beta=1.0, eps=1.0E-15
accuracy: Double = 0.9828725226327379

Note, it's the same 98% we got from our slightly lower-level operations earlier for accuracy.

Think!

What else do you need to investigate to try to understand the mis-predicitons better?

  • time-line?
  • are mis-predictions happening during transitions between users or activities of the same user or both, as our Markov process simply uses the same sliding window over the time-odered, user-grouped, activity streams...
  • ...

Typically, in inustry you will have to improve on an existing algorithm that is in production and getting into the details under the given constraints needs some thinking from scratch over the entire data science pipeline and process.

Explaining the Model's Predictions to a Curious Client whose Activity is being Predicted

Now, let's try to explain the decision branches in each tree of our best-fitted random forest model. Often, being able to "explain" why the model "predicts" is critical for various businesses. how it predicts.

import org.apache.spark.ml.classification.RandomForestClassificationModel
val rfModel = model.stages(2).asInstanceOf[RandomForestClassificationModel]
println(s"Learned classification forest model:\n ${rfModel.toDebugString}")
Learned classification forest model:
 RandomForestClassificationModel: uid=rfc_6ab6b8d21734, numTrees=10, numClasses=5, numFeatures=6
  Tree 0 (weight 1.0):
    If (feature 3 <= 0.45832723868728054)
     If (feature 1 <= -8.097179727272728)
      If (feature 0 <= -7.121753363636364)
       Predict: 2.0
      Else (feature 0 > -7.121753363636364)
       If (feature 5 <= 0.7848413904200169)
        If (feature 1 <= -8.4067287012987)
         If (feature 1 <= -11.596521363636366)
          Predict: 2.0
         Else (feature 1 > -11.596521363636366)
          If (feature 1 <= -9.49238863636364)
           If (feature 0 <= -1.976380909090909)
            Predict: 2.0
           Else (feature 0 > -1.976380909090909)
            Predict: 1.0
          Else (feature 1 > -9.49238863636364)
           Predict: 1.0
        Else (feature 1 > -8.4067287012987)
         If (feature 0 <= -3.502226363636364)
          Predict: 2.0
         Else (feature 0 > -3.502226363636364)
          Predict: 1.0
       Else (feature 5 > 0.7848413904200169)
        Predict: 2.0
     Else (feature 1 > -8.097179727272728)
      If (feature 2 <= 2.943098181818182)
       If (feature 4 <= 0.904496986362019)
        If (feature 3 <= 0.027620762421071275)
         If (feature 0 <= -3.502226363636364)
          Predict: 0.0
         Else (feature 0 > -3.502226363636364)
          If (feature 2 <= -0.045886318181818195)
           If (feature 1 <= -6.820416818181818)
            Predict: 4.0
           Else (feature 1 > -6.820416818181818)
            Predict: 0.0
          Else (feature 2 > -0.045886318181818195)
           Predict: 4.0
        Else (feature 3 > 0.027620762421071275)
         Predict: 4.0
       Else (feature 4 > 0.904496986362019)
        Predict: 2.0
      Else (feature 2 > 2.943098181818182)
       If (feature 3 <= 0.2198889879412786)
        If (feature 0 <= -1.105464818181818)
         Predict: 2.0
        Else (feature 0 > -1.105464818181818)
         If (feature 3 <= 0.12199305012399356)
          Predict: 3.0
         Else (feature 3 > 0.12199305012399356)
          If (feature 1 <= -0.6543302727272726)
           Predict: 3.0
          Else (feature 1 > -0.6543302727272726)
           Predict: 2.0
       Else (feature 3 > 0.2198889879412786)
        If (feature 0 <= -0.1735843181818182)
         Predict: 2.0
        Else (feature 0 > -0.1735843181818182)
         Predict: 3.0
    Else (feature 3 > 0.45832723868728054)
     If (feature 4 <= 2.2658035906051546)
      If (feature 5 <= 2.8353340431585474)
       If (feature 5 <= 0.7848413904200169)
        If (feature 1 <= -8.097179727272728)
         If (feature 3 <= 1.5843984037196344)
          If (feature 0 <= -8.90539)
           Predict: 0.0
          Else (feature 0 > -8.90539)
           If (feature 0 <= 2.8563333333333336)
            If (feature 0 <= -4.357466363636364)
             If (feature 1 <= -8.4067287012987)
              If (feature 2 <= -1.0073777272727273)
               Predict: 1.0
              Else (feature 2 > -1.0073777272727273)
               Predict: 2.0
             Else (feature 1 > -8.4067287012987)
              Predict: 1.0
            Else (feature 0 > -4.357466363636364)
             If (feature 0 <= -2.5093826818181824)
              If (feature 2 <= -0.5126976818181816)
               Predict: 1.0
              Else (feature 2 > -0.5126976818181816)
               Predict: 2.0
             Else (feature 0 > -2.5093826818181824)
              Predict: 1.0
           Else (feature 0 > 2.8563333333333336)
            If (feature 4 <= 0.904496986362019)
             Predict: 1.0
            Else (feature 4 > 0.904496986362019)
             Predict: 2.0
         Else (feature 3 > 1.5843984037196344)
          If (feature 0 <= -8.90539)
           Predict: 0.0
          Else (feature 0 > -8.90539)
           Predict: 2.0
        Else (feature 1 > -8.097179727272728)
         If (feature 3 <= 2.037322122633077)
          If (feature 1 <= -6.820416818181818)
           If (feature 4 <= 0.904496986362019)
            Predict: 4.0
           Else (feature 4 > 0.904496986362019)
            Predict: 2.0
          Else (feature 1 > -6.820416818181818)
           Predict: 2.0
         Else (feature 3 > 2.037322122633077)
          Predict: 0.0
       Else (feature 5 > 0.7848413904200169)
        If (feature 3 <= 3.2305826019123103)
         If (feature 0 <= -8.90539)
          Predict: 0.0
         Else (feature 0 > -8.90539)
          If (feature 1 <= -17.407273636363634)
           Predict: 0.0
          Else (feature 1 > -17.407273636363634)
           If (feature 1 <= -2.2306882272727275)
            If (feature 0 <= -0.5846568636363636)
             If (feature 4 <= 0.904496986362019)
              If (feature 2 <= 0.41744104545454547)
               If (feature 5 <= 1.6130554927490437)
                Predict: 2.0
               Else (feature 5 > 1.6130554927490437)
                If (feature 3 <= 1.7795641834853977)
                 Predict: 2.0
                Else (feature 3 > 1.7795641834853977)
                 If (feature 1 <= -9.105701681818182)
                  If (feature 5 <= 1.7614806708061252)
                   Predict: 2.0
                  Else (feature 5 > 1.7614806708061252)
                   If (feature 5 <= 1.9145738226248412)
                    If (feature 3 <= 2.283530423945612)
                     Predict: 2.0
                    Else (feature 3 > 2.283530423945612)
                     Predict: 1.0
                   Else (feature 5 > 1.9145738226248412)
                    Predict: 2.0
                 Else (feature 1 > -9.105701681818182)
                  If (feature 0 <= -3.065027181818182)
                   If (feature 0 <= -4.988009090909092)
                    Predict: 2.0
                   Else (feature 0 > -4.988009090909092)
                    If (feature 0 <= -3.502226363636364)
                     Predict: 1.0
                    Else (feature 0 > -3.502226363636364)
                     Predict: 2.0
                  Else (feature 0 > -3.065027181818182)
                   Predict: 1.0
              Else (feature 2 > 0.41744104545454547)
               Predict: 2.0
             Else (feature 4 > 0.904496986362019)
              Predict: 2.0
            Else (feature 0 > -0.5846568636363636)
             If (feature 3 <= 1.0884225728208126)
              If (feature 2 <= -0.045886318181818195)
               Predict: 2.0
              Else (feature 2 > -0.045886318181818195)
               Predict: 1.0
             Else (feature 3 > 1.0884225728208126)
              If (feature 4 <= 0.904496986362019)
               If (feature 1 <= -9.49238863636364)
                Predict: 2.0
               Else (feature 1 > -9.49238863636364)
                If (feature 3 <= 1.7795641834853977)
                 If (feature 0 <= 0.32806340909090914)
                  Predict: 2.0
                 Else (feature 0 > 0.32806340909090914)
                  Predict: 1.0
                Else (feature 3 > 1.7795641834853977)
                 Predict: 1.0
              Else (feature 4 > 0.904496986362019)
               Predict: 2.0
           Else (feature 1 > -2.2306882272727275)
            If (feature 2 <= 1.1333349545454543)
             If (feature 0 <= 0.32806340909090914)
              If (feature 1 <= 1.425418909090909)
               Predict: 0.0
              Else (feature 1 > 1.425418909090909)
               Predict: 4.0
             Else (feature 0 > 0.32806340909090914)
              Predict: 0.0
            Else (feature 2 > 1.1333349545454543)
             Predict: 2.0
        Else (feature 3 > 3.2305826019123103)
         If (feature 2 <= -0.9551237727272728)
          If (feature 5 <= 1.4557098485258626)
           If (feature 5 <= 1.2559600735949519)
            Predict: 0.0
           Else (feature 5 > 1.2559600735949519)
            If (feature 0 <= -8.90539)
             Predict: 0.0
            Else (feature 0 > -8.90539)
             Predict: 1.0
          Else (feature 5 > 1.4557098485258626)
           If (feature 3 <= 4.092746328718364)
            If (feature 4 <= 1.9510708064802356)
             If (feature 1 <= -11.596521363636366)
              Predict: 0.0
             Else (feature 1 > -11.596521363636366)
              If (feature 4 <= 1.278422893229283)
               Predict: 2.0
              Else (feature 4 > 1.278422893229283)
               Predict: 0.0
            Else (feature 4 > 1.9510708064802356)
             Predict: 2.0
           Else (feature 3 > 4.092746328718364)
            Predict: 0.0
         Else (feature 2 > -0.9551237727272728)
          If (feature 0 <= 2.8563333333333336)
           If (feature 4 <= 0.904496986362019)
            If (feature 3 <= 3.5937950153207483)
             Predict: 1.0
            Else (feature 3 > 3.5937950153207483)
             Predict: 0.0
           Else (feature 4 > 0.904496986362019)
            If (feature 0 <= -8.90539)
             Predict: 0.0
            Else (feature 0 > -8.90539)
             If (feature 5 <= 2.600144428803959)
              Predict: 2.0
             Else (feature 5 > 2.600144428803959)
              If (feature 4 <= 1.9510708064802356)
               Predict: 0.0
              Else (feature 4 > 1.9510708064802356)
               Predict: 2.0
          Else (feature 0 > 2.8563333333333336)
           If (feature 3 <= 3.5937950153207483)
            If (feature 0 <= 3.5330349999999995)
             Predict: 2.0
            Else (feature 0 > 3.5330349999999995)
             Predict: 0.0
           Else (feature 3 > 3.5937950153207483)
            Predict: 0.0
      Else (feature 5 > 2.8353340431585474)
       If (feature 3 <= 1.0884225728208126)
        If (feature 0 <= -1.976380909090909)
         Predict: 0.0
        Else (feature 0 > -1.976380909090909)
         Predict: 3.0
       Else (feature 3 > 1.0884225728208126)
        If (feature 4 <= 1.9510708064802356)
         If (feature 3 <= 2.283530423945612)
          If (feature 0 <= -8.90539)
           Predict: 0.0
          Else (feature 0 > -8.90539)
           Predict: 2.0
         Else (feature 3 > 2.283530423945612)
          Predict: 0.0
        Else (feature 4 > 1.9510708064802356)
         If (feature 1 <= -10.088093363636364)
          If (feature 1 <= -17.407273636363634)
           Predict: 0.0
          Else (feature 1 > -17.407273636363634)
           Predict: 2.0
         Else (feature 1 > -10.088093363636364)
          Predict: 0.0
     Else (feature 4 > 2.2658035906051546)
      If (feature 3 <= 3.2305826019123103)
       If (feature 4 <= 4.527012376192168)
        If (feature 0 <= 3.5330349999999995)
         If (feature 0 <= -1.2744209090909089)
          If (feature 2 <= -1.8347482272727271)
           If (feature 5 <= 1.4557098485258626)
            If (feature 3 <= 1.5843984037196344)
             Predict: 4.0
            Else (feature 3 > 1.5843984037196344)
             Predict: 0.0
           Else (feature 5 > 1.4557098485258626)
            If (feature 0 <= -4.357466363636364)
             If (feature 0 <= -6.212517272727274)
              Predict: 0.0
             Else (feature 0 > -6.212517272727274)
              If (feature 5 <= 1.9145738226248412)
               If (feature 0 <= -4.988009090909092)
                If (feature 2 <= -2.198210545454545)
                 Predict: 0.0
                Else (feature 2 > -2.198210545454545)
                 Predict: 2.0
               Else (feature 0 > -4.988009090909092)
                Predict: 2.0
              Else (feature 5 > 1.9145738226248412)
               Predict: 2.0
            Else (feature 0 > -4.357466363636364)
             If (feature 1 <= -9.356527272727273)
              If (feature 4 <= 4.0067789684062625)
               If (feature 5 <= 2.0408593821519982)
                Predict: 0.0
               Else (feature 5 > 2.0408593821519982)
                Predict: 2.0
              Else (feature 4 > 4.0067789684062625)
               Predict: 4.0
             Else (feature 1 > -9.356527272727273)
              Predict: 0.0
          Else (feature 2 > -1.8347482272727271)
           If (feature 1 <= -3.8209812727272725)
            If (feature 1 <= -11.596521363636366)
             Predict: 0.0
            Else (feature 1 > -11.596521363636366)
             If (feature 5 <= 0.16873060661442005)
              Predict: 1.0
             Else (feature 5 > 0.16873060661442005)
              If (feature 5 <= 3.469288509552827)
               Predict: 2.0
              Else (feature 5 > 3.469288509552827)
               If (feature 4 <= 3.5166543239603483)
                Predict: 2.0
               Else (feature 4 > 3.5166543239603483)
                Predict: 0.0
           Else (feature 1 > -3.8209812727272725)
            If (feature 4 <= 3.5166543239603483)
             If (feature 2 <= 0.6682646818181818)
              Predict: 0.0
             Else (feature 2 > 0.6682646818181818)
              Predict: 2.0
            Else (feature 4 > 3.5166543239603483)
             Predict: 0.0
         Else (feature 0 > -1.2744209090909089)
          If (feature 2 <= 0.6682646818181818)
           If (feature 1 <= -3.8209812727272725)
            If (feature 5 <= 4.913251092952768)
             Predict: 2.0
            Else (feature 5 > 4.913251092952768)
             Predict: 0.0
           Else (feature 1 > -3.8209812727272725)
            If (feature 3 <= 2.696622839121874)
             Predict: 0.0
            Else (feature 3 > 2.696622839121874)
             If (feature 0 <= -0.1735843181818182)
              Predict: 0.0
             Else (feature 0 > -0.1735843181818182)
              If (feature 5 <= 0.7848413904200169)
               Predict: 4.0
              Else (feature 5 > 0.7848413904200169)
               Predict: 0.0
          Else (feature 2 > 0.6682646818181818)
           If (feature 1 <= -8.948937727272728)
            If (feature 0 <= 0.32806340909090914)
             Predict: 0.0
            Else (feature 0 > 0.32806340909090914)
             Predict: 2.0
           Else (feature 1 > -8.948937727272728)
            Predict: 0.0
        Else (feature 0 > 3.5330349999999995)
         If (feature 0 <= 4.459689318181818)
          If (feature 1 <= -13.810390454545457)
           Predict: 0.0
          Else (feature 1 > -13.810390454545457)
           If (feature 4 <= 2.891537202575433)
            Predict: 2.0
           Else (feature 4 > 2.891537202575433)
            Predict: 0.0
         Else (feature 0 > 4.459689318181818)
          Predict: 0.0
       Else (feature 4 > 4.527012376192168)
        If (feature 4 <= 8.132821942578682)
         If (feature 0 <= -3.502226363636364)
          If (feature 1 <= -11.596521363636366)
           If (feature 2 <= -3.569613363636363)
            Predict: 4.0
           Else (feature 2 > -3.569613363636363)
            If (feature 3 <= 2.9289256343028125)
             Predict: 2.0
            Else (feature 3 > 2.9289256343028125)
             Predict: 0.0
          Else (feature 1 > -11.596521363636366)
           If (feature 2 <= 0.6682646818181818)
            Predict: 0.0
           Else (feature 2 > 0.6682646818181818)
            If (feature 4 <= 6.684054463098245)
             Predict: 0.0
            Else (feature 4 > 6.684054463098245)
             Predict: 2.0
         Else (feature 0 > -3.502226363636364)
          If (feature 1 <= -3.8209812727272725)
           If (feature 0 <= 3.5330349999999995)
            If (feature 5 <= 3.1250203637838814)
             If (feature 2 <= -5.720776181818183)
              Predict: 2.0
             Else (feature 2 > -5.720776181818183)
              If (feature 2 <= 1.1333349545454543)
               If (feature 1 <= -5.109937500000001)
                If (feature 3 <= 1.7795641834853977)
                 Predict: 4.0
                Else (feature 3 > 1.7795641834853977)
                 If (feature 0 <= 0.9882181363636364)
                  If (feature 0 <= 0.5266320454545453)
                   If (feature 2 <= -1.2442670454545455)
                    If (feature 4 <= 5.398982323543355)
                     Predict: 0.0
                    Else (feature 4 > 5.398982323543355)
                     If (feature 5 <= 2.8353340431585474)
                      Predict: 4.0
                     Else (feature 5 > 2.8353340431585474)
                      If (feature 0 <= -1.4538298181818181)
                       If (feature 1 <= -9.49238863636364)
                        Predict: 0.0
                       Else (feature 1 > -9.49238863636364)
                        Predict: 4.0
                      Else (feature 0 > -1.4538298181818181)
                       Predict: 4.0
                   Else (feature 2 > -1.2442670454545455)
                    Predict: 0.0
                  Else (feature 0 > 0.5266320454545453)
                   Predict: 0.0
                 Else (feature 0 > 0.9882181363636364)
                  If (feature 4 <= 6.291886217849433)
                   Predict: 0.0
                  Else (feature 4 > 6.291886217849433)
                   If (feature 1 <= -5.750931181818182)
                    Predict: 4.0
                   Else (feature 1 > -5.750931181818182)
                    If (feature 3 <= 2.283530423945612)
                     Predict: 0.0
                    Else (feature 3 > 2.283530423945612)
                     If (feature 3 <= 2.696622839121874)
                      If (feature 3 <= 2.4887269112897967)
                       Predict: 4.0
                      Else (feature 3 > 2.4887269112897967)
                       Predict: 0.0
                     Else (feature 3 > 2.696622839121874)
                      Predict: 4.0
               Else (feature 1 > -5.109937500000001)
                If (feature 4 <= 5.019055660088064)
                 Predict: 0.0
                Else (feature 4 > 5.019055660088064)
                 If (feature 0 <= -3.065027181818182)
                  Predict: 2.0
                 Else (feature 0 > -3.065027181818182)
                  If (feature 4 <= 7.3665835405207885)
                   Predict: 4.0
                  Else (feature 4 > 7.3665835405207885)
                   Predict: 0.0
              Else (feature 2 > 1.1333349545454543)
               If (feature 3 <= 1.355530712657193)
                Predict: 2.0
               Else (feature 3 > 1.355530712657193)
                If (feature 5 <= 1.6130554927490437)
                 Predict: 0.0
                Else (feature 5 > 1.6130554927490437)
                 If (feature 0 <= -0.3791205454545455)
                  If (feature 4 <= 5.398982323543355)
                   Predict: 0.0
                  Else (feature 4 > 5.398982323543355)
                   Predict: 2.0
                 Else (feature 0 > -0.3791205454545455)
                  Predict: 4.0
            Else (feature 5 > 3.1250203637838814)
             If (feature 2 <= -1.8347482272727271)
              If (feature 1 <= -8.4067287012987)
               If (feature 3 <= 2.283530423945612)
                If (feature 0 <= 0.45695872727272724)
                 If (feature 3 <= 2.037322122633077)
                  If (feature 4 <= 5.019055660088064)
                   Predict: 4.0
                  Else (feature 4 > 5.019055660088064)
                   Predict: 0.0
                 Else (feature 3 > 2.037322122633077)
                  Predict: 2.0
                Else (feature 0 > 0.45695872727272724)
                 Predict: 4.0
               Else (feature 3 > 2.283530423945612)
                Predict: 0.0
              Else (feature 1 > -8.4067287012987)
               If (feature 5 <= 8.699793726565169)
                If (feature 1 <= -6.820416818181818)
                 If (feature 4 <= 7.033163268276285)
                  Predict: 4.0
                 Else (feature 4 > 7.033163268276285)
                  If (feature 3 <= 2.4887269112897967)
                   Predict: 0.0
                  Else (feature 3 > 2.4887269112897967)
                   Predict: 4.0
                Else (feature 1 > -6.820416818181818)
                 Predict: 4.0
               Else (feature 5 > 8.699793726565169)
                Predict: 0.0
             Else (feature 2 > -1.8347482272727271)
              If (feature 5 <= 3.8343025836297375)
               If (feature 1 <= -8.097179727272728)
                Predict: 2.0
               Else (feature 1 > -8.097179727272728)
                If (feature 3 <= 2.9289256343028125)
                 If (feature 3 <= 2.4887269112897967)
                  If (feature 0 <= -3.065027181818182)
                   Predict: 2.0
                  Else (feature 0 > -3.065027181818182)
                   Predict: 0.0
                 Else (feature 3 > 2.4887269112897967)
                  Predict: 0.0
                Else (feature 3 > 2.9289256343028125)
                 Predict: 4.0
              Else (feature 5 > 3.8343025836297375)
               If (feature 2 <= -0.9551237727272728)
                If (feature 5 <= 6.108758959317355)
                 Predict: 4.0
                Else (feature 5 > 6.108758959317355)
                 Predict: 0.0
               Else (feature 2 > -0.9551237727272728)
                Predict: 0.0
           Else (feature 0 > 3.5330349999999995)
            If (feature 4 <= 7.72195028414196)
             Predict: 0.0
            Else (feature 4 > 7.72195028414196)
             If (feature 1 <= -8.712045)
              Predict: 0.0
             Else (feature 1 > -8.712045)
              Predict: 4.0
          Else (feature 1 > -3.8209812727272725)
           If (feature 0 <= -3.065027181818182)
            Predict: 2.0
           Else (feature 0 > -3.065027181818182)
            If (feature 1 <= -2.2306882272727275)
             If (feature 3 <= 2.037322122633077)
              If (feature 5 <= 1.9145738226248412)
               Predict: 4.0
              Else (feature 5 > 1.9145738226248412)
               Predict: 0.0
             Else (feature 3 > 2.037322122633077)
              Predict: 0.0
            Else (feature 1 > -2.2306882272727275)
             Predict: 0.0
        Else (feature 4 > 8.132821942578682)
         If (feature 4 <= 8.97158739539847)
          If (feature 2 <= -1.2442670454545455)
           If (feature 1 <= -3.8209812727272725)
            If (feature 2 <= -5.720776181818183)
             Predict: 0.0
            Else (feature 2 > -5.720776181818183)
             If (feature 0 <= 0.43257299999999993)
              Predict: 4.0
             Else (feature 0 > 0.43257299999999993)
              If (feature 2 <= -2.810174181818182)
               Predict: 4.0
              Else (feature 2 > -2.810174181818182)
               Predict: 0.0
           Else (feature 1 > -3.8209812727272725)
            Predict: 0.0
          Else (feature 2 > -1.2442670454545455)
           If (feature 5 <= 1.9145738226248412)
            If (feature 2 <= 0.1387476818181818)
             Predict: 0.0
            Else (feature 2 > 0.1387476818181818)
             If (feature 0 <= -0.7518725909090909)
              Predict: 0.0
             Else (feature 0 > -0.7518725909090909)
              Predict: 4.0
           Else (feature 5 > 1.9145738226248412)
            Predict: 0.0
         Else (feature 4 > 8.97158739539847)
          Predict: 0.0
      Else (feature 3 > 3.2305826019123103)
       If (feature 1 <= -10.088093363636364)
        If (feature 3 <= 5.42131601555171)
         If (feature 0 <= 2.0089040454545453)
          If (feature 5 <= 4.262646949929151)
           If (feature 0 <= -8.90539)
            Predict: 0.0
           Else (feature 0 > -8.90539)
            If (feature 4 <= 4.527012376192168)
             If (feature 0 <= -0.7518725909090909)
              If (feature 5 <= 1.2559600735949519)
               Predict: 0.0
              Else (feature 5 > 1.2559600735949519)
               Predict: 2.0
             Else (feature 0 > -0.7518725909090909)
              Predict: 0.0
            Else (feature 4 > 4.527012376192168)
             If (feature 4 <= 6.684054463098245)
              Predict: 0.0
             Else (feature 4 > 6.684054463098245)
              If (feature 0 <= 0.32806340909090914)
               If (feature 4 <= 7.3665835405207885)
                If (feature 3 <= 4.596493775946534)
                 Predict: 2.0
                Else (feature 3 > 4.596493775946534)
                 Predict: 0.0
               Else (feature 4 > 7.3665835405207885)
                Predict: 0.0
              Else (feature 0 > 0.32806340909090914)
               Predict: 2.0
          Else (feature 5 > 4.262646949929151)
           Predict: 0.0
         Else (feature 0 > 2.0089040454545453)
          Predict: 0.0
        Else (feature 3 > 5.42131601555171)
         Predict: 0.0
       Else (feature 1 > -10.088093363636364)
        If (feature 5 <= 1.0680362943269028)
         If (feature 4 <= 5.830630767197693)

*** WARNING: skipped 325736 bytes of output ***

                Predict: 2.0
             Else (feature 4 > 5.398982323543355)
              If (feature 0 <= -2.5093826818181824)
               Predict: 4.0
              Else (feature 0 > -2.5093826818181824)
               Predict: 2.0
            Else (feature 1 > -7.698300909090908)
             If (feature 2 <= -1.073569090909091)
              If (feature 3 <= 2.696622839121874)
               If (feature 1 <= -7.295937636363637)
                If (feature 3 <= 1.7795641834853977)
                 Predict: 4.0
                Else (feature 3 > 1.7795641834853977)
                 Predict: 0.0
               Else (feature 1 > -7.295937636363637)
                If (feature 4 <= 4.527012376192168)
                 Predict: 2.0
                Else (feature 4 > 4.527012376192168)
                 Predict: 0.0
              Else (feature 3 > 2.696622839121874)
               Predict: 0.0
             Else (feature 2 > -1.073569090909091)
              Predict: 2.0
         Else (feature 1 > -5.750931181818182)
          If (feature 3 <= 5.42131601555171)
           If (feature 2 <= 6.177680772727272)
            If (feature 1 <= -2.2306882272727275)
             If (feature 3 <= 1.7795641834853977)
              Predict: 4.0
             Else (feature 3 > 1.7795641834853977)
              If (feature 5 <= 1.2559600735949519)
               If (feature 4 <= 2.891537202575433)
                Predict: 2.0
               Else (feature 4 > 2.891537202575433)
                Predict: 0.0
              Else (feature 5 > 1.2559600735949519)
               If (feature 0 <= 2.0089040454545453)
                Predict: 0.0
               Else (feature 0 > 2.0089040454545453)
                If (feature 4 <= 2.891537202575433)
                 Predict: 0.0
                Else (feature 4 > 2.891537202575433)
                 Predict: 4.0
            Else (feature 1 > -2.2306882272727275)
             If (feature 4 <= 3.5166543239603483)
              If (feature 0 <= 0.9882181363636364)
               Predict: 0.0
              Else (feature 0 > 0.9882181363636364)
               If (feature 5 <= 0.7848413904200169)
                Predict: 4.0
               Else (feature 5 > 0.7848413904200169)
                Predict: 0.0
             Else (feature 4 > 3.5166543239603483)
              Predict: 0.0
           Else (feature 2 > 6.177680772727272)
            Predict: 2.0
          Else (feature 3 > 5.42131601555171)
           If (feature 4 <= 5.019055660088064)
            Predict: 0.0
           Else (feature 4 > 5.019055660088064)
            If (feature 3 <= 7.291873594931593)
             If (feature 1 <= -5.109937500000001)
              Predict: 0.0
             Else (feature 1 > -5.109937500000001)
              If (feature 1 <= -2.2306882272727275)
               Predict: 4.0
              Else (feature 1 > -2.2306882272727275)
               Predict: 0.0
            Else (feature 3 > 7.291873594931593)
             Predict: 0.0
       Else (feature 4 > 5.830630767197693)
        If (feature 0 <= -3.065027181818182)
         If (feature 4 <= 7.3665835405207885)
          If (feature 5 <= 1.4557098485258626)
           If (feature 3 <= 3.5937950153207483)
            If (feature 4 <= 6.291886217849433)
             If (feature 0 <= -3.502226363636364)
              Predict: 0.0
             Else (feature 0 > -3.502226363636364)
              Predict: 4.0
            Else (feature 4 > 6.291886217849433)
             Predict: 0.0
           Else (feature 3 > 3.5937950153207483)
            If (feature 2 <= 0.24674104545454545)
             Predict: 4.0
            Else (feature 2 > 0.24674104545454545)
             If (feature 3 <= 5.42131601555171)
              Predict: 4.0
             Else (feature 3 > 5.42131601555171)
              Predict: 0.0
          Else (feature 5 > 1.4557098485258626)
           If (feature 2 <= 0.1387476818181818)
            Predict: 0.0
           Else (feature 2 > 0.1387476818181818)
            If (feature 3 <= 1.0884225728208126)
             Predict: 2.0
            Else (feature 3 > 1.0884225728208126)
             Predict: 4.0
         Else (feature 4 > 7.3665835405207885)
          If (feature 3 <= 4.092746328718364)
           Predict: 0.0
          Else (feature 3 > 4.092746328718364)
           Predict: 4.0
        Else (feature 0 > -3.065027181818182)
         If (feature 1 <= -9.433167272727271)
          If (feature 2 <= -3.569613363636363)
           If (feature 3 <= 2.037322122633077)
            Predict: 4.0
           Else (feature 3 > 2.037322122633077)
            Predict: 2.0
          Else (feature 2 > -3.569613363636363)
           If (feature 0 <= -1.976380909090909)
            If (feature 0 <= -2.5093826818181824)
             Predict: 4.0
            Else (feature 0 > -2.5093826818181824)
             Predict: 2.0
           Else (feature 0 > -1.976380909090909)
            Predict: 0.0
         Else (feature 1 > -9.433167272727271)
          If (feature 3 <= 8.670695907958262)
           If (feature 2 <= 1.1333349545454543)
            If (feature 1 <= -1.1942972727272725)
             If (feature 4 <= 8.97158739539847)
              If (feature 2 <= -0.6624949545454546)
               If (feature 0 <= 7.344164590909091)
                If (feature 2 <= -5.720776181818183)
                 Predict: 0.0
                Else (feature 2 > -5.720776181818183)
                 If (feature 1 <= -2.2306882272727275)
                  If (feature 1 <= -5.750931181818182)
                   Predict: 4.0
                  Else (feature 1 > -5.750931181818182)
                   If (feature 3 <= 2.9289256343028125)
                    If (feature 0 <= 1.2895552272727273)
                     Predict: 4.0
                    Else (feature 0 > 1.2895552272727273)
                     Predict: 0.0
                   Else (feature 3 > 2.9289256343028125)
                    Predict: 4.0
                 Else (feature 1 > -2.2306882272727275)
                  If (feature 5 <= 2.179859408203087)
                   Predict: 4.0
                  Else (feature 5 > 2.179859408203087)
                   Predict: 0.0
               Else (feature 0 > 7.344164590909091)
                If (feature 5 <= 1.7614806708061252)
                 Predict: 4.0
                Else (feature 5 > 1.7614806708061252)
                 Predict: 0.0
              Else (feature 2 > -0.6624949545454546)
               If (feature 4 <= 7.033163268276285)
                If (feature 2 <= -0.5126976818181816)
                 Predict: 4.0
                Else (feature 2 > -0.5126976818181816)
                 If (feature 1 <= -3.8209812727272725)
                  If (feature 2 <= 0.29899645454545454)
                   If (feature 5 <= 1.7614806708061252)
                    Predict: 0.0
                   Else (feature 5 > 1.7614806708061252)
                    Predict: 4.0
                  Else (feature 2 > 0.29899645454545454)
                   Predict: 4.0
                 Else (feature 1 > -3.8209812727272725)
                  Predict: 0.0
               Else (feature 4 > 7.033163268276285)
                If (feature 5 <= 2.0408593821519982)
                 If (feature 1 <= -5.109937500000001)
                  If (feature 3 <= 1.5843984037196344)
                   Predict: 0.0
                  Else (feature 3 > 1.5843984037196344)
                   Predict: 4.0
                 Else (feature 1 > -5.109937500000001)
                  Predict: 0.0
                Else (feature 5 > 2.0408593821519982)
                 If (feature 0 <= 3.5330349999999995)
                  If (feature 1 <= -5.750931181818182)
                   If (feature 3 <= 2.037322122633077)
                    Predict: 0.0
                   Else (feature 3 > 2.037322122633077)
                    Predict: 4.0
                  Else (feature 1 > -5.750931181818182)
                   Predict: 0.0
                 Else (feature 0 > 3.5330349999999995)
                  If (feature 5 <= 2.179859408203087)
                   Predict: 4.0
                  Else (feature 5 > 2.179859408203087)
                   Predict: 0.0
             Else (feature 4 > 8.97158739539847)
              Predict: 0.0
            Else (feature 1 > -1.1942972727272725)
             Predict: 0.0
           Else (feature 2 > 1.1333349545454543)
            If (feature 1 <= -5.750931181818182)
             If (feature 0 <= 0.9882181363636364)
              If (feature 5 <= 1.7614806708061252)
               Predict: 0.0
              Else (feature 5 > 1.7614806708061252)
               Predict: 2.0
             Else (feature 0 > 0.9882181363636364)
              Predict: 4.0
            Else (feature 1 > -5.750931181818182)
             Predict: 0.0
          Else (feature 3 > 8.670695907958262)
           Predict: 0.0
      Else (feature 5 > 2.600144428803959)
       If (feature 3 <= 3.2305826019123103)
        If (feature 0 <= 2.0089040454545453)
         If (feature 1 <= -7.698300909090908)
          If (feature 5 <= 6.108758959317355)
           If (feature 1 <= -11.596521363636366)
            If (feature 0 <= -8.90539)
             Predict: 0.0
            Else (feature 0 > -8.90539)
             If (feature 0 <= -1.976380909090909)
              If (feature 3 <= 2.9289256343028125)
               If (feature 5 <= 3.8343025836297375)
                Predict: 4.0
               Else (feature 5 > 3.8343025836297375)
                Predict: 2.0
              Else (feature 3 > 2.9289256343028125)
               Predict: 0.0
             Else (feature 0 > -1.976380909090909)
              If (feature 4 <= 7.033163268276285)
               Predict: 2.0
              Else (feature 4 > 7.033163268276285)
               Predict: 0.0
           Else (feature 1 > -11.596521363636366)
            If (feature 2 <= -2.4757429090909095)
             If (feature 3 <= 2.037322122633077)
              Predict: 4.0
             Else (feature 3 > 2.037322122633077)
              If (feature 4 <= 6.291886217849433)
               Predict: 2.0
              Else (feature 4 > 6.291886217849433)
               Predict: 0.0
            Else (feature 2 > -2.4757429090909095)
             If (feature 4 <= 6.684054463098245)
              Predict: 2.0
             Else (feature 4 > 6.684054463098245)
              If (feature 1 <= -10.088093363636364)
               Predict: 2.0
              Else (feature 1 > -10.088093363636364)
               If (feature 0 <= -4.214637727272727)
                Predict: 2.0
               Else (feature 0 > -4.214637727272727)
                Predict: 0.0
          Else (feature 5 > 6.108758959317355)
           If (feature 1 <= -9.276403181818182)
            Predict: 0.0
           Else (feature 1 > -9.276403181818182)
            If (feature 2 <= -3.569613363636363)
             Predict: 4.0
            Else (feature 2 > -3.569613363636363)
             Predict: 0.0
         Else (feature 1 > -7.698300909090908)
          If (feature 4 <= 6.684054463098245)
           If (feature 4 <= 3.5166543239603483)
            If (feature 1 <= -5.109937500000001)
             Predict: 2.0
            Else (feature 1 > -5.109937500000001)
             If (feature 2 <= 1.1333349545454543)
              Predict: 0.0
             Else (feature 2 > 1.1333349545454543)
              Predict: 2.0
           Else (feature 4 > 3.5166543239603483)
            If (feature 3 <= 1.7795641834853977)
             If (feature 5 <= 3.469288509552827)
              If (feature 0 <= -3.065027181818182)
               If (feature 1 <= -3.8209812727272725)
                Predict: 2.0
               Else (feature 1 > -3.8209812727272725)
                Predict: 0.0
              Else (feature 0 > -3.065027181818182)
               Predict: 4.0
             Else (feature 5 > 3.469288509552827)
              Predict: 0.0
            Else (feature 3 > 1.7795641834853977)
             If (feature 1 <= -7.295937636363637)
              Predict: 2.0
             Else (feature 1 > -7.295937636363637)
              If (feature 4 <= 4.0067789684062625)
               If (feature 0 <= -1.105464818181818)
                Predict: 0.0
               Else (feature 0 > -1.105464818181818)
                Predict: 2.0
              Else (feature 4 > 4.0067789684062625)
               Predict: 0.0
          Else (feature 4 > 6.684054463098245)
           If (feature 1 <= -3.8209812727272725)
            If (feature 5 <= 8.699793726565169)
             If (feature 3 <= 1.5843984037196344)
              Predict: 0.0
             Else (feature 3 > 1.5843984037196344)
              If (feature 2 <= -1.073569090909091)
               If (feature 5 <= 4.262646949929151)
                Predict: 4.0
               Else (feature 5 > 4.262646949929151)
                If (feature 0 <= 0.9882181363636364)
                 If (feature 2 <= -2.198210545454545)
                  Predict: 4.0
                 Else (feature 2 > -2.198210545454545)
                  If (feature 0 <= 0.43257299999999993)
                   Predict: 4.0
                  Else (feature 0 > 0.43257299999999993)
                   Predict: 0.0
                Else (feature 0 > 0.9882181363636364)
                 Predict: 4.0
              Else (feature 2 > -1.073569090909091)
               If (feature 3 <= 2.4887269112897967)
                Predict: 2.0
               Else (feature 3 > 2.4887269112897967)
                Predict: 0.0
            Else (feature 5 > 8.699793726565169)
             Predict: 0.0
           Else (feature 1 > -3.8209812727272725)
            If (feature 5 <= 3.469288509552827)
             Predict: 2.0
            Else (feature 5 > 3.469288509552827)
             Predict: 0.0
        Else (feature 0 > 2.0089040454545453)
         If (feature 5 <= 2.8353340431585474)
          If (feature 2 <= -5.720776181818183)
           Predict: 2.0
          Else (feature 2 > -5.720776181818183)
           Predict: 0.0
         Else (feature 5 > 2.8353340431585474)
          If (feature 4 <= 4.0067789684062625)
           If (feature 3 <= 2.283530423945612)
            If (feature 1 <= -13.810390454545457)
             Predict: 0.0
            Else (feature 1 > -13.810390454545457)
             If (feature 2 <= -1.2442670454545455)
              Predict: 2.0
             Else (feature 2 > -1.2442670454545455)
              Predict: 0.0
           Else (feature 3 > 2.283530423945612)
            Predict: 0.0
          Else (feature 4 > 4.0067789684062625)
           If (feature 5 <= 3.1250203637838814)
            If (feature 3 <= 2.9289256343028125)
             Predict: 0.0
            Else (feature 3 > 2.9289256343028125)
             If (feature 0 <= 2.8563333333333336)
              Predict: 4.0
             Else (feature 0 > 2.8563333333333336)
              Predict: 0.0
           Else (feature 5 > 3.1250203637838814)
            Predict: 0.0
       Else (feature 3 > 3.2305826019123103)
        If (feature 3 <= 4.596493775946534)
         If (feature 1 <= -8.097179727272728)
          If (feature 5 <= 3.469288509552827)
           If (feature 3 <= 3.5937950153207483)
            If (feature 5 <= 2.8353340431585474)
             Predict: 0.0
            Else (feature 5 > 2.8353340431585474)
             If (feature 0 <= 2.0089040454545453)
              If (feature 4 <= 5.398982323543355)
               If (feature 0 <= -8.90539)
                Predict: 0.0
               Else (feature 0 > -8.90539)
                Predict: 2.0
              Else (feature 4 > 5.398982323543355)
               Predict: 2.0
             Else (feature 0 > 2.0089040454545453)
              Predict: 0.0
           Else (feature 3 > 3.5937950153207483)
            If (feature 2 <= -0.6624949545454546)
             Predict: 0.0
            Else (feature 2 > -0.6624949545454546)
             If (feature 0 <= 2.0089040454545453)
              If (feature 4 <= 7.3665835405207885)
               If (feature 5 <= 3.1250203637838814)
                Predict: 2.0
               Else (feature 5 > 3.1250203637838814)
                Predict: 0.0
              Else (feature 4 > 7.3665835405207885)
               Predict: 0.0
             Else (feature 0 > 2.0089040454545453)
              Predict: 0.0
          Else (feature 5 > 3.469288509552827)
           If (feature 3 <= 4.092746328718364)
            Predict: 0.0
           Else (feature 3 > 4.092746328718364)
            If (feature 4 <= 7.72195028414196)
             Predict: 0.0
            Else (feature 4 > 7.72195028414196)
             If (feature 1 <= -11.596521363636366)
              If (feature 5 <= 4.262646949929151)
               Predict: 2.0
              Else (feature 5 > 4.262646949929151)
               Predict: 0.0
             Else (feature 1 > -11.596521363636366)
              If (feature 1 <= -8.4067287012987)
               Predict: 0.0
              Else (feature 1 > -8.4067287012987)
               If (feature 0 <= 1.2895552272727273)
                Predict: 0.0
               Else (feature 0 > 1.2895552272727273)
                Predict: 4.0
         Else (feature 1 > -8.097179727272728)
          If (feature 1 <= -3.8209812727272725)
           If (feature 2 <= -1.5194759545454544)
            If (feature 4 <= 5.830630767197693)
             Predict: 0.0
            Else (feature 4 > 5.830630767197693)
             If (feature 5 <= 6.108758959317355)
              If (feature 2 <= -5.720776181818183)
               Predict: 0.0
              Else (feature 2 > -5.720776181818183)
               If (feature 0 <= -0.7518725909090909)
                Predict: 0.0
               Else (feature 0 > -0.7518725909090909)
                Predict: 4.0
             Else (feature 5 > 6.108758959317355)
              Predict: 0.0
           Else (feature 2 > -1.5194759545454544)
            If (feature 2 <= -0.18174913636363638)
             If (feature 1 <= -5.750931181818182)
              Predict: 0.0
             Else (feature 1 > -5.750931181818182)
              If (feature 0 <= -7.121753363636364)
               Predict: 0.0
              Else (feature 0 > -7.121753363636364)
               Predict: 4.0
            Else (feature 2 > -0.18174913636363638)
             If (feature 0 <= 2.0089040454545453)
              If (feature 2 <= 1.1333349545454543)
               If (feature 0 <= -1.976380909090909)
                If (feature 0 <= -4.165866818181819)
                 Predict: 2.0
                Else (feature 0 > -4.165866818181819)
                 Predict: 0.0
               Else (feature 0 > -1.976380909090909)
                Predict: 2.0
              Else (feature 2 > 1.1333349545454543)
               Predict: 0.0
             Else (feature 0 > 2.0089040454545453)
              If (feature 0 <= 4.459689318181818)
               Predict: 4.0
              Else (feature 0 > 4.459689318181818)
               Predict: 0.0
          Else (feature 1 > -3.8209812727272725)
           If (feature 2 <= 0.6682646818181818)
            Predict: 0.0
           Else (feature 2 > 0.6682646818181818)
            If (feature 4 <= 3.5166543239603483)
             Predict: 2.0
            Else (feature 4 > 3.5166543239603483)
             Predict: 0.0
        Else (feature 3 > 4.596493775946534)
         If (feature 4 <= 6.291886217849433)
          If (feature 2 <= -0.6624949545454546)
           If (feature 5 <= 2.8353340431585474)
            If (feature 0 <= 0.43257299999999993)
             Predict: 0.0
            Else (feature 0 > 0.43257299999999993)
             If (feature 3 <= 8.670695907958262)
              If (feature 3 <= 6.490709433033732)
               Predict: 4.0
              Else (feature 3 > 6.490709433033732)
               If (feature 3 <= 7.291873594931593)
                Predict: 0.0
               Else (feature 3 > 7.291873594931593)
                Predict: 4.0
             Else (feature 3 > 8.670695907958262)
              Predict: 0.0
           Else (feature 5 > 2.8353340431585474)
            If (feature 1 <= -6.820416818181818)
             If (feature 1 <= -7.295937636363637)
              Predict: 0.0
             Else (feature 1 > -7.295937636363637)
              If (feature 2 <= -1.8347482272727271)
               Predict: 0.0
              Else (feature 2 > -1.8347482272727271)
               If (feature 2 <= -1.073569090909091)
                Predict: 2.0
               Else (feature 2 > -1.073569090909091)
                Predict: 0.0
            Else (feature 1 > -6.820416818181818)
             Predict: 0.0
          Else (feature 2 > -0.6624949545454546)
           If (feature 1 <= -8.948937727272728)
            Predict: 0.0
           Else (feature 1 > -8.948937727272728)
            If (feature 3 <= 5.42131601555171)
             If (feature 0 <= 0.32806340909090914)
              If (feature 1 <= -6.2386456818181815)
               If (feature 0 <= -3.065027181818182)
                Predict: 0.0
               Else (feature 0 > -3.065027181818182)
                If (feature 5 <= 4.262646949929151)
                 Predict: 2.0
                Else (feature 5 > 4.262646949929151)
                 Predict: 0.0
              Else (feature 1 > -6.2386456818181815)
               Predict: 2.0
             Else (feature 0 > 0.32806340909090914)
              Predict: 0.0
            Else (feature 3 > 5.42131601555171)
             If (feature 2 <= -0.5126976818181816)
              If (feature 3 <= 5.87583214563006)
               If (feature 4 <= 5.019055660088064)
                Predict: 0.0
               Else (feature 4 > 5.019055660088064)
                Predict: 2.0
              Else (feature 3 > 5.87583214563006)
               Predict: 0.0
             Else (feature 2 > -0.5126976818181816)
              Predict: 0.0
         Else (feature 4 > 6.291886217849433)
          If (feature 5 <= 2.8353340431585474)
           If (feature 4 <= 7.72195028414196)
            If (feature 0 <= 5.969858363636364)
             If (feature 0 <= -7.121753363636364)
              Predict: 0.0
             Else (feature 0 > -7.121753363636364)
              Predict: 4.0
            Else (feature 0 > 5.969858363636364)
             Predict: 0.0
           Else (feature 4 > 7.72195028414196)
            Predict: 0.0
          Else (feature 5 > 2.8353340431585474)
           If (feature 3 <= 5.42131601555171)
            If (feature 2 <= -1.073569090909091)
             If (feature 5 <= 4.913251092952768)
              If (feature 0 <= 2.8563333333333336)
               If (feature 4 <= 7.3665835405207885)
                Predict: 0.0
               Else (feature 4 > 7.3665835405207885)
                If (feature 0 <= -5.695193636363635)
                 Predict: 2.0
                Else (feature 0 > -5.695193636363635)
                 Predict: 4.0
              Else (feature 0 > 2.8563333333333336)
               Predict: 0.0
             Else (feature 5 > 4.913251092952768)
              Predict: 0.0
            Else (feature 2 > -1.073569090909091)
             If (feature 5 <= 4.262646949929151)
              If (feature 2 <= -0.18174913636363638)
               If (feature 5 <= 3.8343025836297375)
                Predict: 0.0
               Else (feature 5 > 3.8343025836297375)
                Predict: 2.0
              Else (feature 2 > -0.18174913636363638)
               Predict: 0.0
             Else (feature 5 > 4.262646949929151)
              Predict: 0.0
           Else (feature 3 > 5.42131601555171)
            If (feature 1 <= -8.948937727272728)
             Predict: 0.0
            Else (feature 1 > -8.948937727272728)
             If (feature 1 <= -8.712045)
              If (feature 3 <= 5.87583214563006)
               Predict: 4.0
              Else (feature 3 > 5.87583214563006)
               Predict: 0.0
             Else (feature 1 > -8.712045)
              If (feature 2 <= -0.6624949545454546)
               If (feature 5 <= 3.1250203637838814)
                If (feature 3 <= 8.670695907958262)
                 If (feature 3 <= 6.490709433033732)
                  Predict: 4.0
                 Else (feature 3 > 6.490709433033732)
                  If (feature 4 <= 7.033163268276285)
                   Predict: 0.0
                  Else (feature 4 > 7.033163268276285)
                   If (feature 2 <= -1.0073777272727273)
                    If (feature 1 <= -5.109937500000001)
                     Predict: 4.0
                    Else (feature 1 > -5.109937500000001)
                     Predict: 0.0
                   Else (feature 2 > -1.0073777272727273)
                    Predict: 0.0
                Else (feature 3 > 8.670695907958262)
                 Predict: 0.0
               Else (feature 5 > 3.1250203637838814)
                Predict: 0.0
              Else (feature 2 > -0.6624949545454546)
               Predict: 0.0

import org.apache.spark.ml.classification.RandomForestClassificationModel
rfModel: org.apache.spark.ml.classification.RandomForestClassificationModel = RandomForestClassificationModel: uid=rfc_6ab6b8d21734, numTrees=10, numClasses=5, numFeatures=6

Save and Load later to Serve Predictions

When you are satisfied with the model you have trained/fitted then you can save it to a file and load it again from another low-latency prediciton-serving system to serve predictions.

model
res24: org.apache.spark.ml.PipelineModel = pipeline_dd3e9eb4d47c
import org.apache.spark.ml.PipelineModel
import org.apache.spark.ml.PipelineModel

Save the model to a file in stable storage.

model.write.overwrite().save("/datasets/sds/ActivityRecognition/preTrainedModels/myRandomForestClassificationModelAsPipeLineModel")

Load the model, typically from a prediction or model serving layer/system.

val same_rfModelFromSavedFile = PipelineModel.load("/datasets/sds/ActivityRecognition/preTrainedModels/myRandomForestClassificationModelAsPipeLineModel")
same_rfModelFromSavedFile: org.apache.spark.ml.PipelineModel = pipeline_dd3e9eb4d47c
same_rfModelFromSavedFile
res26: org.apache.spark.ml.PipelineModel = pipeline_dd3e9eb4d47c

Suppose new data is coming at us and we need to serve our predicitons of the activities

Note: We only need accelerometer readings so prediciton pipeline can be simplified to only take in the needed features for prediction. For simplicity let's assume the test data is representative of the new data (previously unseen) that is coming at us for serving our activity predicitons.

val newDataForPrediction = testData.sample(0.0004,12348L) // get a random test data as new data for prediction
display(newDataForPrediction.select("meanX", "meanY", "meanZ", "stddevX", "stddevY","stddevZ")) // showing only features that will be used by model for prediction
meanX meanY meanZ stddevX stddevY stddevZ
-1.9955399999999999 -9.258980909090907 1.0410163636363636 1.0549255357138732 0.7680301427703919 1.8853035398286844

Here is another new data coming at you... you can predict the current activity being done by simply transforming the loaded model (estimator).

val newDataForPrediction = testData.sample(0.0004,1234L) // get a random test data as new data for prediction
display(newDataForPrediction.select("meanX", "meanY", "meanZ", "stddevX", "stddevY","stddevZ")) // showing only features that will be used by model for prediction
meanX meanY meanZ stddevX stddevY stddevZ
0.42212218181818173 -0.7135524545454545 9.440134545454546 8.409472091286836e-2 9.073949633706861e-2 9.389382640736067e-2
display(same_rfModelFromSavedFile.transform(newDataForPrediction).select("meanX", "meanY", "meanZ", "stddevX", "stddevY","stddevZ","prediction"))
meanX meanY meanZ stddevX stddevY stddevZ prediction
0.42212218181818173 -0.7135524545454545 9.440134545454546 8.409472091286836e-2 9.073949633706861e-2 9.389382640736067e-2 3.0

Some minor post-processing to connect prediction label to the activity string.

Typically one prediction is just a small part of larger business or science use-case.

activityLabelDF.show
+--------+-----+
|activity|label|
+--------+-----+
| Jogging|  0.0|
| Jumping|  4.0|
|Standing|  1.0|
| Walking|  2.0|
| Sitting|  3.0|
+--------+-----+
display(same_rfModelFromSavedFile
        .transform(newDataForPrediction)
        .select("meanX", "meanY", "meanZ", "stddevX", "stddevY","stddevZ","prediction")
        .join(activityLabelDF,$"prediction"===$"label")
        .drop("prediction","label")
        .withColumnRenamed("activity","Your current activity is likely to be")
       )
meanX meanY meanZ stddevX stddevY stddevZ Your current activity is likely to be
0.42212218181818173 -0.7135524545454545 9.440134545454546 8.409472091286836e-2 9.073949633706861e-2 9.389382640736067e-2 Sitting

An activity-based music-recommendation system - a diatribe:

For example, you may want to correlate historical music-listening habits for a user with their historical physical activities and then recommend music to them using a subsequent recommender system pipeline that uses activity prediciton as one of its input.

NOTE: One has to be legally compliant for using the data in such manner with client consent, depending on the jurisdiction of your operations - GDPR applies for EU operations, for example --- this is coming attraction!

display(same_rfModelFromSavedFile.transform(testData.sample(0.01))) // note more can be done with such data, time of day can be informative for other decision problems
  1. Download and Load Data

The following anonymized dataset is used with kind permission of Amira Lakhal.

wget http://lamastex.org/datasets/public/ActivityRecognition/dataTraining.csv
--2020-11-13 09:48:32--  http://lamastex.org/datasets/public/ActivityRecognition/dataTraining.csv
Resolving lamastex.org (lamastex.org)... 166.62.28.100
Connecting to lamastex.org (lamastex.org)|166.62.28.100|:80... connected.
HTTP request sent, awaiting response... 200 OK
Length: 931349 (910K) [text/csv]
Saving to: ‘dataTraining.csv’

     0K .......... .......... .......... .......... ..........  5%  140K 6s
    50K .......... .......... .......... .......... .......... 10%  282K 4s
   100K .......... .......... .......... .......... .......... 16%  288K 4s
   150K .......... .......... .......... .......... .......... 21% 14.8M 3s
   200K .......... .......... .......... .......... .......... 27% 33.2M 2s
   250K .......... .......... .......... .......... .......... 32%  287K 2s
   300K .......... .......... .......... .......... .......... 38% 35.0M 1s
   350K .......... .......... .......... .......... .......... 43% 35.7M 1s
   400K .......... .......... .......... .......... .......... 49% 48.3M 1s
   450K .......... .......... .......... .......... .......... 54%  293K 1s
   500K .......... .......... .......... .......... .......... 60% 20.8M 1s
   550K .......... .......... .......... .......... .......... 65% 44.5M 1s
   600K .......... .......... .......... .......... .......... 71% 39.1M 0s
   650K .......... .......... .......... .......... .......... 76% 44.6M 0s
   700K .......... .......... .......... .......... .......... 82% 41.9M 0s
   750K .......... .......... .......... .......... .......... 87% 42.0M 0s
   800K .......... .......... .......... .......... .......... 93% 42.4M 0s
   850K .......... .......... .......... .......... .......... 98%  297K 0s
   900K .........                                             100% 35.8M=1.2s

2020-11-13 09:48:33 (734 KB/s) - ‘dataTraining.csv’ saved [931349/931349]
pwd && ls
/databricks/driver
conf
dataTraining.csv
derby.log
eventlogs
ganglia
logs
//dbutils.fs.mkdirs("dbfs:///datasets/sds/ActivityRecognition") // make directory if needed
dbutils.fs.mv("file:///databricks/driver/dataTraining.csv","dbfs:///datasets/sds/ActivityRecognition/dataTraining.csv")
res25: Boolean = true
display(dbutils.fs.ls("dbfs:///datasets/sds/ActivityRecognition"))
path name size
dbfs:/datasets/sds/ActivityRecognition/dataTraining.csv dataTraining.csv 931349.0
dbutils.fs.head("dbfs:///datasets/sds/ActivityRecognition/dataTraining.csv")
[Truncated to first 65536 bytes]
res27: String =
"user_id","activity","timeStampAsLong","x","y","z"
"user_001","Jumping",1446047227606,"4.33079","-12.72175","-3.18118"
"user_001","Jumping",1446047227671,"0.575403","-0.727487","2.95007"
"user_001","Jumping",1446047227735,"-1.60885","3.52607","-0.1922"
"user_001","Jumping",1446047227799,"0.690364","-0.037722","1.72382"
"user_001","Jumping",1446047227865,"3.44943","-1.68549","2.29862"
"user_001","Jumping",1446047227930,"1.87829","-1.91542","0.880768"
"user_001","Jumping",1446047227995,"1.57173","-5.86241","-3.75599"
"user_001","Jumping",1446047228059,"3.41111","-17.93331","0.535886"
"user_001","Jumping",1446047228123,"3.18118","-19.58108","5.74745"
"user_001","Jumping",1446047228189,"7.85626","-19.2362","0.804128"
"user_001","Jumping",1446047228253,"1.26517","-8.85139","2.18366"
"user_001","Jumping",1446047228318,"0.077239","1.15021","1.53221"
"user_001","Jumping",1446047228383,"0.230521","2.0699","-1.41845"
"user_001","Jumping",1446047228447,"0.652044","-0.497565","1.76214"
"user_001","Jumping",1446047228512,"1.53341","-0.305964","1.41725"
"user_001","Jumping",1446047228578,"-1.07237","-1.95374","0.191003"
"user_001","Jumping",1446047228642,"2.75966","-13.75639","0.191003"
"user_001","Jumping",1446047228707,"7.43474","-19.58108","2.95007"
"user_001","Jumping",1446047228771,"5.63368","-19.58108","5.59417"
"user_001","Jumping",1446047228836,"5.02056","-11.72542","-1.38013"
"user_001","Jumping",1446047228900,"-2.10702","0.575403","1.07237"
"user_001","Jumping",1446047228966,"-1.30229","2.2615","-1.26517"
"user_001","Jumping",1446047229030,"1.68669","-0.957409","1.57053"
"user_001","Jumping",1446047229095,"2.60638","-0.229323","2.14534"
"user_001","Jumping",1446047229159,"1.30349","-0.152682","0.497565"
"user_001","Jumping",1446047229224,"1.64837","-8.12331","1.60885"
"user_001","Jumping",1446047229290,"0.15388","-18.46979","-1.03525"
"user_001","Jumping",1446047229354,"4.98224","-19.58108","0.995729"
"user_001","Jumping",1446047229419,"5.17384","-19.2362","0.612526"
"user_001","Jumping",1446047229483,"2.03158","-9.11964","1.34061"
"user_001","Jumping",1446047229549,"-1.95374","-1.03405","0.574206"
"user_001","Jumping",1446047229612,"0.1922","1.30349","-1.03525"
"user_001","Jumping",1446047229678,"1.64837","-0.727487","-0.307161"
"user_001","Jumping",1446047229743,"2.56806","-1.03405","0.267643"
"user_001","Jumping",1446047229806,"1.41845","-0.305964","0.727487"
"user_001","Jumping",1446047229872,"1.03525","-6.82042","0.957409"
"user_001","Jumping",1446047229936,"3.94759","-19.31284","-1.22685"
"user_001","Jumping",1446047230001,"6.13185","-19.58108","2.72014"
"user_001","Jumping",1446047230066,"7.89458","-16.9753","0.229323"
"user_001","Jumping",1446047230131,"2.6447","-3.75479","0.114362"
"user_001","Jumping",1446047230195,"-2.41358","1.91661","-0.000599"
"user_001","Jumping",1446047230260,"-1.95374","-0.114362","-0.268841"
"user_001","Jumping",1446047230325,"-0.229323","-1.95374","2.75846"
"user_001","Jumping",1446047230390,"2.68302","0.268841","0.535886"
"user_001","Jumping",1446047230455,"1.15021","-1.41725","0.880768"
"user_001","Jumping",1446047230519,"2.98958","-11.53382","-0.920286"
"user_001","Jumping",1446047230584,"8.00954","-19.58108","-0.1922"
"user_001","Jumping",1446047230649,"7.31978","-19.58108","2.52854"
"user_001","Jumping",1446047230713,"5.44208","-13.56479","-0.498763"
"user_001","Jumping",1446047230779,"0.728685","-0.420925","1.68549"
"user_001","Jumping",1446047230842,"1.18853","1.41845","-2.22318"
"user_001","Jumping",1446047230907,"0.15388","-1.80046","2.03038"
"user_001","Jumping",1446047230972,"-0.037722","1.07357","-0.958607"
"user_001","Jumping",1446047231038,"0.230521","0.728685","-0.690364"
"user_001","Jumping",1446047231102,"0.805325","-1.14901","1.53221"
"user_001","Jumping",1446047231167,"5.17384","-9.15796","-2.91294"
"user_001","Jumping",1446047231231,"8.00954","-19.54276","1.49389"
"user_001","Jumping",1446047231296,"11.61165","-19.58108","4.25296"
"user_001","Jumping",1446047231361,"7.89458","-18.35483","3.71647"
"user_001","Jumping",1446047231426,"0.537083","-3.21831","0.420925"
"user_001","Jumping",1446047231490,"-1.91542","4.10087","-2.6447"
"user_001","Jumping",1446047231555,"-0.919089","-0.382604","0.114362"
"user_001","Jumping",1446047231620,"0.613724","-0.842448","1.57053"
"user_001","Jumping",1446047231684,"1.38013","-0.459245","0.305964"
"user_001","Jumping",1446047231749,"2.29982","-1.49389","-1.26517"
"user_001","Jumping",1446047231814,"4.94392","-10.95901","-0.498763"
"user_001","Jumping",1446047231878,"3.75599","-19.27452","-1.76333"
"user_001","Jumping",1446047231944,"7.70298","-19.58108","-2.95126"
"user_001","Jumping",1446047232008,"6.55337","-17.51178","-1.91661"
"user_001","Jumping",1446047232073,"2.10822","-2.03038","-0.268841"
"user_001","Jumping",1446047232138,"-1.68549","3.67935","-0.881966"
"user_001","Jumping",1446047232203,"0.15388","-0.114362","0.076042"
"user_001","Jumping",1446047232267,"2.79798","-1.95374","0.689167"
"user_001","Jumping",1446047232332,"1.45677","-0.957409","0.420925"
"user_001","Jumping",1446047232397,"1.18853","-2.95007","0.650847"
"user_001","Jumping",1446047232462,"3.44943","-13.87135","-3.71767"
"user_001","Jumping",1446047232526,"3.79431","-19.58108","-0.345482"
"user_001","Jumping",1446047232591,"6.09353","-19.58108","2.87342"
"user_001","Jumping",1446047232655,"4.48408","-14.3312","-0.498763"
"user_001","Jumping",1446047232720,"-0.037722","-1.68549","2.6435"
"user_001","Jumping",1446047232785,"0.613724","2.68302","-2.37646"
"user_001","Jumping",1446047232850,"0.996927","-0.497565","0.497565"
"user_001","Jumping",1446047232915,"0.15388","-0.689167","1.34061"
"user_001","Jumping",1446047232979,"1.07357","1.07357","-2.60638"
"user_001","Jumping",1446047233044,"2.37646","-3.29495","-1.45677"
"user_001","Jumping",1446047233109,"2.22318","-16.09393","1.37893"
"user_001","Jumping",1446047233173,"6.82161","-19.58108","0.037722"
"user_001","Jumping",1446047233238,"8.39275","-19.54276","1.22565"
"user_001","Jumping",1446047233303,"1.22685","-9.50284","-0.307161"
"user_001","Jumping",1446047233368,"1.83997","-0.152682","1.41725"
"user_001","Jumping",1446047233432,"-0.765807","0.996927","-1.91661"
"user_001","Jumping",1446047233497,"0.728685","-0.612526","0.152682"
"user_001","Jumping",1446047233562,"0.996927","-0.305964","0.995729"
"user_001","Jumping",1446047233626,"1.22685","-0.305964","0.037722"
"user_001","Jumping",1446047233692,"1.91661","-2.95007","-0.345482"
"user_001","Jumping",1446047233755,"4.75232","-14.63776","-3.67935"
"user_001","Jumping",1446047233821,"4.56072","-19.58108","-2.6447"
"user_001","Jumping",1446047233886,"10.69197","-19.38948","-5.94025"
"user_001","Jumping",1446047233950,"3.10454","-10.42253","-2.22318"
"user_001","Jumping",1446047234015,"-0.152682","1.61005","1.80046"
"user_001","Jumping",1446047234080,"-0.267643","1.83997","-0.958607"
"user_001","Jumping",1446047234145,"1.99325","-0.842448","-0.230521"
"user_001","Jumping",1446047234210,"2.79798","-0.114362","0.919089"
"user_001","Jumping",1446047234273,"1.11189","-0.152682","1.83878"
"user_001","Jumping",1446047234339,"2.75966","-5.05768","-0.537083"
"user_001","Jumping",1446047234403,"4.33079","-16.82202","-3.06622"
"user_001","Jumping",1446047234468,"6.89825","-19.58108","-4.25415"
"user_001","Jumping",1446047234533,"11.49669","-19.50444","-2.52974"
"user_001","Jumping",1446047234598,"6.20849","-9.08132","-1.80165"
"user_001","Jumping",1446047234663,"0.805325","1.15021","-0.15388"
"user_001","Jumping",1446047234726,"-1.76214","2.14654","-0.460442"
"user_001","Jumping",1446047234792,"0.000599","-1.11069","-0.230521"
"user_001","Jumping",1446047234857,"0.652044","0.230521","-0.920286"
"user_001","Jumping",1446047234922,"1.26517","-0.114362","-0.000599"
"user_001","Jumping",1446047234986,"5.36544","-4.09967","-0.537083"
"user_001","Jumping",1446047235051,"6.51505","-17.05194","-3.56439"
"user_001","Jumping",1446047235115,"6.93658","-19.58108","-2.75966"
"user_001","Jumping",1446047235181,"7.89458","-19.58108","-3.18118"
"user_001","Jumping",1446047235245,"1.95493","-9.6178","-1.34181"
"user_001","Jumping",1446047235310,"-2.18366","3.14286","-0.1922"
"user_001","Jumping",1446047235375,"-2.87342","1.99325","-1.76333"
"user_001","Jumping",1446047235439,"1.03525","-1.80046","1.64717"
"user_001","Jumping",1446047235504,"1.95493","-0.689167","1.49389"
"user_001","Jumping",1446047235569,"1.26517","0.383802","-0.307161"
"user_001","Jumping",1446047235633,"1.18853","-2.72014","1.41725"
"user_001","Jumping",1446047235698,"5.71033","-16.51545","-2.03158"
"user_001","Jumping",1446047235763,"6.55337","-19.58108","0.995729"
"user_001","Jumping",1446047235828,"10.577","-19.4278","-1.57173"
"user_001","Jumping",1446047235892,"2.79798","-9.88604","-0.843646"
"user_001","Jumping",1446047235957,"0.652044","-0.037722","1.14901"
"user_001","Jumping",1446047236022,"0.843646","1.95493","-2.14654"
"user_001","Jumping",1446047236086,"0.15388","-0.305964","0.995729"
"user_001","Jumping",1446047236152,"0.767005","-0.114362","0.804128"
"user_001","Jumping",1446047236215,"-0.650847","-0.650847","-0.230521"
"user_001","Jumping",1446047236281,"3.56439","-5.90073","0.727487"
"user_001","Jumping",1446047236346,"7.05154","-17.97163","-1.61005"
"user_001","Jumping",1446047236410,"9.46572","-19.58108","2.10702"
"user_001","Jumping",1446047236475,"7.58802","-18.54643","3.10335"
"user_001","Jumping",1446047236540,"0.767005","-6.28393","0.689167"
"user_001","Jumping",1446047236604,"0.307161","2.29982","-0.498763"
"user_001","Jumping",1446047236669,"0.11556","-0.114362","-1.11189"
"user_001","Jumping",1446047236734,"2.2615","-1.45557","2.14534"
"user_001","Jumping",1446047236798,"1.80165","0.345482","0.765807"
"user_001","Jumping",1446047236863,"-0.650847","-0.305964","-1.15021"
"user_001","Jumping",1446047236928,"3.48775","-7.31858","-0.728685"
"user_001","Jumping",1446047236992,"5.32712","-18.92964","0.114362"
"user_001","Jumping",1446047237057,"10.34708","-19.58108","2.37526"
"user_001","Jumping",1446047237122,"5.97857","-17.78002","0.344284"
"user_001","Jumping",1446047237187,"2.8363","-3.25663","0.152682"
"user_001","Jumping",1446047237252,"-0.995729","3.37279","-1.64837"
"user_001","Jumping",1446047237317,"-1.64717","-0.650847","1.41725"
"user_001","Jumping",1446047237381,"1.30349","-0.152682","1.45557"
"user_001","Jumping",1446047237446,"2.79798","0.000599","-0.460442"
"user_001","Jumping",1446047237510,"1.41845","-0.459245","-1.38013"
"user_001","Jumping",1446047237575,"3.90927","-6.62882","-1.49509"
"user_001","Jumping",1446047237640,"4.98224","-19.27452","1.57053"
"user_001","Jumping",1446047237705,"12.22478","-19.58108","2.0687"
"user_001","Jumping",1446047237769,"4.5224","-16.74538","-0.383802"
"user_001","Jumping",1446047237834,"0.690364","-0.880768","-0.537083"
"user_001","Jumping",1446047237899,"1.26517","2.18486","-1.03525"
"user_001","Jumping",1446047237964,"2.6447","-0.037722","1.18733"
"user_001","Jumping",1446047238028,"2.56806","-0.114362","1.03405"
"user_001","Jumping",1446047238094,"-1.14901","0.11556","-0.307161"
"user_001","Jumping",1446047238157,"-0.574206","-0.114362","-0.920286"
"user_001","Jumping",1446047238223,"2.60638","-3.40991","-0.422122"
"user_001","Jumping",1446047238287,"6.32345","-17.62674","-0.728685"
"user_001","Jumping",1446047238352,"10.53868","-19.58108","0.919089"
"user_001","Jumping",1446047238417,"7.85626","-18.20155","0.995729"
"user_001","Jumping",1446047238481,"-0.152682","-1.41725","-1.22685"
"user_001","Jumping",1446047238546,"1.26517","2.22318","-1.87829"
"user_001","Jumping",1446047238611,"0.537083","-0.497565","1.76214"
"user_001","Jumping",1446047238676,"1.95493","0.230521","1.60885"
"user_001","Jumping",1446047238741,"0.920286","0.537083","-0.422122"
"user_001","Jumping",1446047238806,"0.000599","-0.650847","0.497565"
"user_001","Jumping",1446047238870,"1.64837","-1.99206","-1.72501"
"user_001","Jumping",1446047238935,"5.0972","-14.75272","-1.41845"
"user_001","Jumping",1446047239000,"10.50036","-19.58108","1.91542"
"user_001","Jumping",1446047239064,"8.16283","-19.58108","1.95374"
"user_001","Jumping",1446047239129,"3.56439","-9.4262","-1.22685"
"user_001","Jumping",1446047239194,"0.920286","2.79798","-1.34181"
"user_001","Jumping",1446047239259,"0.1922","0.652044","-0.537083"
"user_001","Jumping",1446047239324,"1.64837","-0.957409","1.41725"
"user_001","Jumping",1446047239388,"1.99325","-0.191003","0.957409"
"user_001","Jumping",1446047239453,"1.26517","-0.305964","-0.000599"
"user_001","Jumping",1446047239518,"2.4531","-4.17632","-1.34181"
"user_001","Jumping",1446047239583,"4.44576","-16.05561","-0.537083"
"user_001","Jumping",1446047239647,"9.58068","-19.58108","1.53221"
"user_001","Jumping",1446047239712,"8.04786","-19.2362","2.0687"
"user_001","Jumping",1446047239777,"1.80165","-6.01569","-0.422122"
"user_001","Jumping",1446047239841,"0.11556","2.10822","-2.6447"
"user_001","Jumping",1446047239906,"0.345482","-0.612526","-1.22685"
"user_001","Jumping",1446047239971,"1.45677","-0.880768","2.2603"
"user_001","Jumping",1446047240036,"0.843646","1.11189","-0.537083"
"user_001","Jumping",1446047240100,"0.996927","0.038919","-0.575403"
"user_001","Jumping",1446047240166,"3.29615","-3.98471","-0.422122"
"user_001","Jumping",1446047240231,"5.21216","-16.7837","-0.613724"
"user_001","Jumping",1446047240295,"7.39642","-19.58108","1.11069"
"user_001","Jumping",1446047240360,"10.23212","-19.58108","0.459245"
"user_001","Jumping",1446047240424,"1.80165","-12.14694","-1.22685"
"user_001","Jumping",1446047240489,"0.575403","1.83997","0.037722"
"user_001","Jumping",1446047240553,"-0.152682","2.22318","-3.0279"
"user_001","Jumping",1446047240618,"0.268841","-1.91542","3.06503"
"user_001","Jumping",1446047240683,"1.72501","-0.535886","1.83878"
"user_001","Jumping",1446047240748,"-1.18733","0.996927","-1.26517"
"user_001","Jumping",1446047240813,"0.920286","-0.535886","-1.91661"
"user_001","Jumping",1446047240878,"4.40743","-11.61046","0.459245"
"user_001","Jumping",1446047240941,"6.78329","-19.58108","4.82776"
"user_001","Jumping",1446047241007,"9.35075","-19.58108","5.74745"
"user_001","Jumping",1446047241072,"5.71033","-15.74905","-1.15021"
"user_001","Jumping",1446047241136,"-1.57053","-1.80046","-0.15388"
"user_001","Jumping",1446047241201,"-0.267643","2.18486","-2.14654"
"user_001","Jumping",1446047241266,"2.22318","-1.80046","1.80046"
"user_001","Jumping",1446047241330,"-1.34061","0.767005","-2.03158"
"user_001","Jumping",1446047241395,"-0.382604","-0.842448","0.382604"
"user_001","Jumping",1446047241459,"-0.765807","-1.41725","0.076042"
"user_001","Jumping",1446047241525,"5.97857","-10.34589","-1.49509"
"user_001","Jumping",1446047241589,"11.34341","-19.58108","6.13065"
"user_001","Jumping",1446047241654,"10.15548","-19.58108","8.58315"
"user_001","Jumping",1446047241718,"4.67568","-11.61046","-0.307161"
"user_001","Jumping",1446047241783,"-1.37893","-0.650847","0.459245"
"user_001","Jumping",1446047241849,"-0.919089","2.6447","-3.14286"
"user_001","Jumping",1446047241913,"1.07357","-1.03405","-0.613724"
"user_001","Jumping",1446047241977,"0.15388","-0.919089","2.18366"
"user_001","Jumping",1446047242042,"-0.995729","0.460442","0.305964"
"user_001","Jumping",1446047242107,"2.03158","-0.382604","0.076042"
"user_001","Jumping",1446047242172,"6.93658","-10.84405","-0.422122"
"user_001","Jumping",1446047242237,"13.79591","-19.58108","1.49389"
"user_001","Jumping",1446047242302,"15.86521","-19.50444","-1.72501"
"user_001","Jumping",1446047242366,"4.79064","-12.03198","1.8771"
"user_001","Jumping",1446047242431,"-0.497565","1.45677","-4.10087"
"user_001","Jumping",1446047242495,"0.11556","0.613724","-1.30349"
"user_001","Jumping",1446047242560,"-0.459245","-0.305964","2.56686"
"user_001","Jumping",1446047242625,"2.29982","1.18853","-0.767005"
"user_001","Jumping",1446047242690,"1.38013","-0.305964","-1.87829"
"user_001","Jumping",1446047242754,"2.52974","-2.75846","0.152682"
"user_001","Jumping",1446047242819,"5.32712","-13.21991","-1.34181"
"user_001","Jumping",1446047242884,"10.50036","-19.58108","1.8771"
"user_001","Jumping",1446047242948,"13.02951","-19.58108","-0.498763"
"user_001","Jumping",1446047243013,"4.33079","-10.34589","-2.4531"
"user_001","Jumping",1446047243078,"0.613724","0.498763","2.49022"
"user_001","Jumping",1446047243143,"0.307161","1.53341","-2.49142"
"user_001","Jumping",1446047243207,"0.077239","-0.344284","1.91542"
"user_001","Jumping",1446047243272,"2.03158","0.1922","-0.000599"
"user_001","Jumping",1446047243337,"1.22685","0.230521","-1.87829"
"user_001","Jumping",1446047243401,"0.537083","-1.26397","0.535886"
"user_001","Jumping",1446047243467,"5.2888","-11.22725","0.689167"
"user_001","Jumping",1446047243531,"11.57333","-19.58108","0.344284"
"user_001","Jumping",1446047243596,"14.524","-19.58108","2.33694"
"user_001","Jumping",1446047243661,"3.18118","-11.8787","0.191003"
"user_001","Jumping",1446047243725,"-1.07237","1.15021","0.152682"
"user_001","Jumping",1446047243790,"0.422122","1.95493","-1.87829"
"user_001","Jumping",1446047243855,"-0.535886","-0.957409","1.18733"
"user_001","Jumping",1446047243920,"3.60271","-0.114362","0.574206"
"user_001","Jumping",1446047243984,"2.87462","-0.535886","-0.268841"
"user_001","Jumping",1446047244049,"2.2615","-1.53221","-0.11556"
"user_001","Jumping",1446047244114,"6.85994","-10.61413","-1.11189"
"user_001","Jumping",1446047244178,"7.97122","-19.58108","-0.077239"
"user_001","Jumping",1446047244243,"14.86888","-19.58108","-1.41845"
"user_001","Jumping",1446047244308,"8.50771","-14.48448","-0.613724"
"user_001","Jumping",1446047244373,"-0.535886","-1.18733","1.64717"
"user_001","Jumping",1446047244437,"-4.5212","3.37279","0.191003"
"user_001","Jumping",1446047244502,"-1.72382","0.690364","0.191003"
"user_003","Jumping",1446047778034,"-2.75846","-7.28026","-1.45677"
"user_003","Jumping",1446047778099,"-3.75479","-7.08866","-2.37646"
"user_003","Jumping",1446047778164,"-2.14534","-6.74378","-2.22318"
"user_003","Jumping",1446047778229,"-2.22198","-6.01569","-2.2615"
"user_003","Jumping",1446047778293,"-3.63983","-9.04299","-2.6447"
"user_003","Jumping",1446047778358,"-4.82776","-17.09026","-4.02423"
"user_003","Jumping",1446047778422,"-5.82409","-19.46612","-6.70665"
"user_003","Jumping",1446047778488,"0.805325","-10.92069","-1.49509"
"user_003","Jumping",1446047778552,"-4.67448","1.22685","1.64717"
"user_003","Jumping",1446047778616,"-1.37893","0.460442","-2.18486"
"user_003","Jumping",1446047778682,"0.1922","-0.650847","-0.077239"
"user_003","Jumping",1446047778746,"-0.842448","0.11556","-1.26517"
"user_003","Jumping",1446047778811,"-1.26397","-11.91702","-3.64103"
"user_003","Jumping",1446047778876,"-1.41725","-19.58108","-0.767005"
"user_003","Jumping",1446047778940,"-1.76214","-15.44249","-2.68302"
"user_003","Jumping",1446047779006,"-0.574206","-9.00468","-1.76333"
"user_003","Jumping",1446047779071,"-3.14167","-4.36792","-1.68669"
"user_003","Jumping",1446047779135,"-3.37159","-4.3296","-2.4531"
"user_003","Jumping",1446047779200,"-4.06135","-4.75112","-3.10454"
"user_003","Jumping",1446047779265,"-4.36792","-11.26557","-0.345482"
"user_003","Jumping",1446047779329,"-5.97737","-19.12124","-4.25415"
"user_003","Jumping",1446047779394,"-3.75479","-19.19788","-4.9056"
"user_003","Jumping",1446047779459,"-0.459245","-7.39522","-0.537083"
"user_003","Jumping",1446047779524,"-2.91174","3.10454","-2.37646"
"user_003","Jumping",1446047779589,"-1.41725","-0.995729","-0.230521"
"user_003","Jumping",1446047779653,"0.422122","-0.114362","0.344284"
"user_003","Jumping",1446047779718,"-0.574206","-0.535886","-1.18853"
"user_003","Jumping",1446047779783,"-1.72382","-13.98632","-4.10087"
"user_003","Jumping",1446047779847,"-3.14167","-19.58108","-3.48775"
"user_003","Jumping",1446047779912,"-2.68182","-13.21991","-3.18118"
"user_003","Jumping",1446047779977,"-0.267643","-8.92803","-2.10822"
"user_003","Jumping",1446047780042,"-3.17999","-3.98471","-0.728685"
"user_003","Jumping",1446047780107,"-2.91174","-4.48288","-2.18486"
"user_003","Jumping",1446047780171,"-3.37159","-5.78577","-3.87095"
"user_003","Jumping",1446047780236,"-4.02303","-9.84772","-0.383802"
"user_003","Jumping",1446047780301,"-6.47553","-17.81835","-4.13919"
"user_003","Jumping",1446047780365,"-3.86975","-19.58108","-5.40376"
"user_003","Jumping",1446047780430,"-1.99206","-14.44616","-3.64103"
"user_003","Jumping",1446047780495,"-2.29862","-1.18733","-0.307161"
"user_003","Jumping",1446047780559,"-1.8771","1.99325","-1.68669"
"user_003","Jumping",1446047780625,"0.000599","-0.344284","0.650847"
"user_003","Jumping",1446047780689,"-0.459245","-0.191003","-0.613724"
"user_003","Jumping",1446047780754,"-2.60518","-6.9737","-4.714"
"user_003","Jumping",1446047780818,"-1.41725","-19.58108","-2.56806"
"user_003","Jumping",1446047780884,"-3.40991","-17.51178","-4.59904"
"user_003","Jumping",1446047780948,"-1.95374","-10.61413","-2.91294"
"user_003","Jumping",1446047781013,"-3.06503","-6.70546","-1.76333"
"user_003","Jumping",1446047781078,"-2.6435","-7.20362","-1.87829"
"user_003","Jumping",1446047781143,"-2.60518","-7.28026","-1.64837"
"user_003","Jumping",1446047781208,"-1.72382","-6.51385","-2.0699"
"user_003","Jumping",1446047781272,"-0.689167","-5.55585","-2.37646"
"user_003","Jumping",1446047781337,"-3.67815","-8.00835","-1.99325"
"user_003","Jumping",1446047781402,"-5.63249","-13.64143","-3.44943"
"user_003","Jumping",1446047781467,"-5.97737","-18.16323","-5.59536"
"user_003","Jumping",1446047781531,"-2.03038","-19.2362","-5.25048"
"user_003","Jumping",1446047781596,"-2.14534","-8.88971","-1.18853"
"user_003","Jumping",1446047781660,"-3.06503","2.52974","-0.767005"
"user_003","Jumping",1446047781725,"0.230521","0.268841","-0.345482"
"user_003","Jumping",1446047781790,"0.15388","-0.535886","-0.690364"
"user_003","Jumping",1446047781855,"-0.420925","-2.18366","-2.68302"
"user_003","Jumping",1446047781919,"-3.63983","-17.47346","-4.44576"
"user_003","Jumping",1446047781985,"-2.91174","-18.35483","-4.714"
"user_003","Jumping",1446047782049,"-0.919089","-10.88237","-2.2615"
"user_003","Jumping",1446047782114,"-3.02671","-6.93538","-2.68302"
"user_003","Jumping",1446047782178,"-2.75846","-7.3569","-2.10822"
"user_003","Jumping",1446047782244,"-1.45557","-7.85507","-1.22685"
"user_003","Jumping",1446047782309,"-1.8771","-6.32225","-1.99325"
"user_003","Jumping",1446047782373,"-1.64717","-5.90073","-2.33814"
"user_003","Jumping",1446047782438,"-2.49022","-8.08499","-1.80165"
"user_003","Jumping",1446047782503,"-4.40624","-11.26557","-2.37646"
"user_003","Jumping",1446047782568,"-5.13432","-17.1669","-4.67568"
"user_003","Jumping",1446047782632,"-3.40991","-19.54276","-5.71033"
"user_003","Jumping",1446047782697,"-1.99206","-13.48815","-4.06255"
"user_003","Jumping",1446047782762,"-2.22198","-1.68549","0.267643"
"user_003","Jumping",1446047782827,"-1.91542","1.80165","-1.68669"
"user_003","Jumping",1446047782891,"0.575403","-0.152682","0.459245"
"user_003","Jumping",1446047782956,"-0.842448","-0.804128","-1.03525"
"user_003","Jumping",1446047783021,"-1.76214","-12.22358","-5.67201"
"user_003","Jumping",1446047783086,"-2.33694","-19.19788","-4.02423"
"user_003","Jumping",1446047783151,"-1.14901","-14.98264","-4.13919"
"user_003","Jumping",1446047783215,"-2.22198","-9.04299","-2.91294"
"user_003","Jumping",1446047783280,"-2.41358","-5.59417","-0.613724"
"user_003","Jumping",1446047783344,"-2.60518","-5.78577","-2.33814"
"user_003","Jumping",1446047783409,"-3.67815","-4.44456","-2.4531"
"user_003","Jumping",1446047783474,"-2.8351","-4.63616","-3.75599"
"user_003","Jumping",1446047783539,"-1.64717","-16.4005","-0.843646"
"user_003","Jumping",1446047783604,"-6.62882","-19.58108","-8.58435"
"user_003","Jumping",1446047783669,"-1.72382","-14.67608","-3.52607"
"user_003","Jumping",1446047783733,"-1.57053","1.34181","0.612526"
"user_003","Jumping",1446047783798,"-1.18733","1.22685","-1.38013"
"user_003","Jumping",1446047783863,"-0.612526","-0.612526","-0.268841"
"user_003","Jumping",1446047783928,"-1.22565","0.345482","-0.805325"
"user_003","Jumping",1446047783992,"-1.11069","-2.2603","-2.56806"
"user_003","Jumping",1446047784057,"-2.8351","-17.62674","-5.02056"
"user_003","Jumping",1446047784122,"-3.90807","-19.19788","-5.59536"
"user_003","Jumping",1446047784187,"-1.72382","-12.6451","-3.64103"
"user_003","Jumping",1446047784252,"-1.49389","-6.7821","-2.0699"
"user_003","Jumping",1446047784316,"-2.14534","-4.67448","-1.15021"
"user_003","Jumping",1446047784381,"-2.91174","-6.93538","-2.6447"
"user_003","Jumping",1446047784446,"-3.71647","-5.86241","-2.56806"
"user_003","Jumping",1446047784510,"-0.344284","-6.51385","-2.8363"
"user_003","Jumping",1446047784575,"-4.02303","-14.98264","-2.2615"
"user_003","Jumping",1446047784639,"-5.36425","-19.58108","-8.89091"
"user_003","Jumping",1446047784704,"-0.191003","-14.906","-3.94759"
"user_003","Jumping",1446047784769,"-2.4519","0.077239","1.11069"
"user_003","Jumping",1446047784834,"-2.4519","1.22685","-1.41845"
"user_003","Jumping",1446047784899,"-0.344284","0.345482","-0.15388"
"user_003","Jumping",1446047784964,"-0.842448","0.422122","-0.996927"
"user_003","Jumping",1446047785029,"-2.29862","-4.3296","-4.63736"
"user_003","Jumping",1446047785093,"-0.765807","-18.92964","-3.98591"
"user_003","Jumping",1446047785158,"-4.3296","-19.38948","-5.17384"
"user_003","Jumping",1446047785222,"-1.11069","-12.6451","-1.22685"
"user_003","Jumping",1446047785287,"-3.44823","-7.24194","-2.18486"
"user_003","Jumping",1446047785352,"-2.49022","-6.51385","-2.95126"
"user_003","Jumping",1446047785417,"-2.10702","-6.85874","-1.22685"
"user_003","Jumping",1446047785482,"-2.79678","-7.05034","-2.14654"
"user_003","Jumping",1446047785546,"-2.56686","-5.01936","-2.52974"
"user_003","Jumping",1446047785611,"-2.87342","-6.62882","-2.56806"
"user_003","Jumping",1446047785676,"-4.63616","-14.44616","-2.52974"
"user_003","Jumping",1446047785741,"-5.67081","-19.58108","-6.59169"
"user_003","Jumping",1446047785805,"-3.67815","-17.66507","-6.63001"
"user_003","Jumping",1446047785870,"-0.919089","-4.82776","-0.268841"
"user_003","Jumping",1446047785934,"-2.91174","2.87462","-2.33814"
"user_003","Jumping",1446047785999,"-0.420925","-0.420925","0.919089"
"user_003","Jumping",1446047786065,"-0.037722","0.230521","0.382604"
"user_003","Jumping",1446047786129,"-0.842448","-0.497565","-3.0279"
"user_003","Jumping",1446047786194,"-0.995729","-15.48081","-4.33079"
"user_003","Jumping",1446047786259,"-3.98471","-19.50444","-6.89825"
"user_003","Jumping",1446047786324,"-0.574206","-13.29655","-3.94759"
"user_003","Jumping",1446047786388,"-1.41725","-8.85139","-1.38013"
"user_003","Jumping",1446047786453,"-3.94639","-5.59417","-3.14286"
"user_003","Jumping",1446047786518,"-2.18366","-8.04667","-3.06622"
"user_003","Jumping",1446047786582,"-1.60885","-8.92803","-1.15021"
"user_003","Jumping",1446047786647,"-2.72014","-5.13432","-2.33814"
"user_003","Jumping",1446047786712,"-2.03038","-4.25296","-3.18118"
"user_003","Jumping",1446047786777,"-3.48655","-9.84772","-1.45677"
"user_003","Jumping",1446047786841,"-6.01569","-18.96796","-6.78329"
"user_003","Jumping",1446047786906,"-4.44456","-19.4278","-8.62267"
"user_003","Jumping",1446047786970,"-0.267643","-8.92803","-1.57173"
"user_003","Jumping",1446047787035,"-2.91174","3.41111","-1.53341"
"user_003","Jumping",1446047787100,"0.268841","-0.765807","0.689167"
"user_003","Jumping",1446047787165,"-0.650847","0.383802","-0.728685"
"user_003","Jumping",1446047787230,"-0.880768","0.422122","-1.03525"
"user_003","Jumping",1446047787294,"-1.60885","-11.11229","-5.4804"
"user_003","Jumping",1446047787358,"-4.59784","-19.35116","-5.94025"
"user_003","Jumping",1446047787424,"-2.41358","-15.71073","-5.74865"
"user_003","Jumping",1446047787489,"-1.26397","-9.34956","-3.06622"
"user_003","Jumping",1446047787553,"-3.44823","-6.47553","-2.75966"
"user_003","Jumping",1446047787618,"-2.4519","-7.97003","-2.2615"
"user_003","Jumping",1446047787683,"-1.95374","-7.81675","-1.83997"
"user_003","Jumping",1446047787747,"-2.75846","-4.67448","-3.06622"
"user_003","Jumping",1446047787812,"-2.22198","-5.24928","-2.0699"
"user_003","Jumping",1446047787877,"-3.29495","-12.41518","-1.49509"
"user_003","Jumping",1446047787942,"-5.44089","-19.46612","-6.20849"
"user_003","Jumping",1446047788007,"-3.79311","-18.69972","-7.70298"
"user_003","Jumping",1446047788071,"-0.382604","-7.1653","-1.83997"
"user_003","Jumping",1446047788136,"-3.14167","2.72134","-0.575403"
"user_003","Jumping",1446047788201,"0.460442","-0.152682","0.114362"
"user_003","Jumping",1446047788265,"-0.842448","0.652044","-0.230521"
"user_003","Jumping",1446047788331,"-2.2603","-0.229323","-1.45677"
"user_003","Jumping",1446047788395,"-1.45557","-13.71807","-6.63001"
"user_003","Jumping",1446047788460,"-3.14167","-19.54276","-6.32345"
"user_003","Jumping",1446047788524,"-1.83878","-13.06663","-4.40743"
"user_003","Jumping",1446047788590,"-1.83878","-9.77108","-3.25783"
"user_003","Jumping",1446047788654,"-3.14167","-6.55217","-2.6447"
"user_003","Jumping",1446047788719,"-2.10702","-7.31858","-2.10822"
"user_003","Jumping",1446047788784,"-2.14534","-5.90073","-2.0699"
"user_003","Jumping",1446047788848,"-1.57053","-4.9044","-2.75966"
"user_003","Jumping",1446047788913,"-2.75846","-7.5485","-1.76333"
"user_003","Jumping",1446047788978,"-4.98104","-15.97897","-4.67568"
"user_003","Jumping",1446047789043,"-3.10335","-19.58108","-8.16283"
"user_003","Jumping",1446047789107,"-1.68549","-16.36218","-5.25048"
"user_003","Jumping",1446047789172,"-2.52854","-2.0687","-0.345482"
"user_003","Jumping",1446047789236,"-1.72382","2.41478","-2.37646"
"user_003","Jumping",1446047789301,"0.843646","-0.382604","1.11069"
"user_003","Jumping",1446047789366,"-0.689167","0.230521","-0.728685"
"user_003","Jumping",1446047789431,"-1.14901","-1.95374","-2.72134"
"user_003","Jumping",1446047789495,"-3.90807","-17.74171","-7.58802"
"user_003","Jumping",1446047789560,"-3.29495","-18.96796","-5.05888"
"user_003","Jumping",1446047789625,"-2.22198","-12.0703","-3.98591"
"user_003","Jumping",1446047789690,"-2.79678","-7.7401","-2.37646"
"user_003","Jumping",1446047789755,"-1.95374","-5.74745","-2.22318"
"user_003","Jumping",1446047789818,"-2.03038","-6.85874","-1.68669"
"user_003","Jumping",1446047789883,"-2.91174","-5.67081","-2.52974"
"user_003","Jumping",1446047789949,"-1.49389","-4.94272","-2.75966"
"user_003","Jumping",1446047790013,"-3.37159","-10.88237","-1.57173"
"user_003","Jumping",1446047790078,"-5.51753","-19.58108","-7.24314"
"user_003","Jumping",1446047790143,"-4.48288","-17.5501","-6.9749"
"user_003","Jumping",1446047790207,"-0.612526","-2.68182","-0.613724"
"user_003","Jumping",1446047790272,"-1.8771","2.68302","-2.03158"
"user_003","Jumping",1446047790337,"1.15021","-0.919089","1.64717"
"user_003","Jumping",1446047790402,"-2.03038","0.307161","-1.22685"
"user_003","Jumping",1446047790467,"-1.34061","-0.191003","-1.61005"
"user_003","Jumping",1446047790531,"-3.02671","-13.64143","-5.17384"
"user_003","Jumping",1446047790596,"-4.75112","-19.58108","-7.62634"
"user_003","Jumping",1446047790660,"-2.60518","-15.05928","-6.01689"
"user_003","Jumping",1446047790726,"-1.26397","-8.12331","-3.10454"
"user_003","Jumping",1446047790790,"-3.25663","-5.97737","-3.0279"
"user_003","Jumping",1446047790855,"-0.420925","-6.24561","-2.2615"
"user_003","Jumping",1446047790919,"-1.83878","-3.40991","-3.60271"
"user_003","Jumping",1446047790984,"-3.94639","-5.36425","-3.75599"
"user_003","Jumping",1446047791049,"-2.2603","-13.98632","-3.67935"
"user_003","Jumping",1446047791114,"-7.70178","-19.58108","-7.5497"
"user_003","Jumping",1446047791179,"-2.52854","-15.36585","-6.66833"
"user_003","Jumping",1446047791243,"-0.574206","-0.497565","-0.230521"
"user_003","Jumping",1446047791308,"-2.0687","0.958607","-0.575403"
"user_003","Jumping",1446047791373,"0.11556","-0.497565","0.344284"
"user_003","Jumping",1446047791438,"-1.30229","1.34181","-1.11189"
"user_003","Jumping",1446047791503,"-0.382604","-0.880768","-2.22318"
"user_003","Jumping",1446047791568,"-2.87342","-15.97897","-6.28513"
"user_003","Jumping",1446047791632,"-2.95007","-19.38948","-7.51138"
"user_003","Jumping",1446047791697,"-4.59784","-13.37319","-5.02056"
"user_003","Jumping",1446047791762,"-2.14534","-9.84772","-3.2195"
"user_003","Jumping",1446047791827,"-2.29862","-6.55217","-2.49142"
"user_003","Jumping",1446047791891,"-1.68549","-7.47186","-2.29982"
"user_003","Jumping",1446047791956,"-1.22565","-8.16163","-2.56806"
"user_003","Jumping",1446047792021,"-2.95007","-5.096","-2.52974"
"user_003","Jumping",1446047792085,"-4.02303","-4.06135","-7.7413"
"user_003","Jumping",1446047792151,"-2.60518","-14.40784","0.727487"
"user_003","Jumping",1446047792215,"-6.24561","-19.58108","-8.89091"
"user_003","Jumping",1446047792280,"-1.60885","-12.56846","-3.2195"
"user_003","Jumping",1446047792344,"-3.10335","3.14286","-1.26517"
"user_003","Jumping",1446047792410,"-0.037722","0.000599","-0.11556"
"user_003","Jumping",1446047792474,"0.268841","-0.650847","0.114362"
"user_003","Jumping",1446047792539,"-2.68182","0.996927","-1.99325"
"user_003","Jumping",1446047792603,"-1.64717","-4.67448","-5.51872"
"user_003","Jumping",1446047792669,"-2.87342","-18.96796","-5.86361"
"user_003","Jumping",1446047792733,"-3.29495","-18.66139","-4.44576"
"user_003","Jumping",1446047792798,"-4.02303","-13.21991","-4.79064"
"user_003","Jumping",1446047792863,"-2.95007","-7.97003","-2.79798"
"user_003","Jumping",1446047792928,"-3.17999","-6.20729","-2.29982"
"user_003","Jumping",1446047792992,"-3.25663","-5.40257","-2.37646"
"user_003","Jumping",1446047793057,"-3.40991","-4.5212","-3.18118"
"user_003","Jumping",1446047793122,"-3.29495","-3.90807","-3.94759"
"user_003","Jumping",1446047793186,"-4.7128","-14.7144","-2.75966"
"user_003","Jumping",1446047793251,"-4.55952","-19.58108","-7.77962"
"user_003","Jumping",1446047793316,"-2.95007","-16.32385","-6.93658"
"user_003","Jumping",1446047793380,"-1.26397","-2.14534","-1.38013"
"user_003","Jumping",1446047793445,"-2.10702","2.33814","-1.64837"
"user_003","Jumping",1446047793510,"-0.420925","-0.267643","1.07237"
"user_003","Jumping",1446047793575,"-0.995729","0.383802","-0.537083"
"user_003","Jumping",1446047793640,"-1.14901","-1.76214","-2.29982"
"user_003","Jumping",1446047793704,"-2.56686","-14.82936","-6.28513"
"user_003","Jumping",1446047793768,"-3.40991","-19.31284","-7.3581"
"user_003","Jumping",1446047793834,"-3.52487","-13.87135","-5.63368"
"user_003","Jumping",1446047793899,"-2.68182","-10.84405","-3.10454"
"user_003","Jumping",1446047793963,"-2.72014","-4.78944","-2.72134"
"user_003","Jumping",1446047794028,"-1.03405","-4.94272","-1.68669"
"user_003","Jumping",1446047794093,"-2.10702","-5.93905","-2.14654"
"user_003","Jumping",1446047794158,"-1.57053","-5.90073","-3.2195"
"user_003","Jumping",1446047794222,"-4.3296","-8.08499","-1.15021"
"user_003","Jumping",1446047794287,"-4.48288","-19.08292","-6.36177"
"user_003","Jumping",1446047794352,"-4.67448","-19.58108","-8.27779"
"user_003","Jumping",1446047794416,"0.000599","-10.76741","-2.33814"
"user_003","Jumping",1446047794481,"-1.95374","3.41111","-1.07357"
"user_003","Jumping",1446047794546,"-0.152682","-0.689167","0.229323"
"user_003","Jumping",1446047794611,"-0.957409","0.422122","-0.460442"
"user_003","Jumping",1446047794676,"-0.957409","0.996927","-0.881966"
"user_003","Jumping",1446047794740,"-1.57053","-3.60151","-4.75232"
"user_003","Jumping",1446047794805,"-1.99206","-18.35483","-5.78697"
"user_003","Jumping",1446047794870,"-3.71647","-19.2362","-6.47673"
"user_003","Jumping",1446047794935,"-0.842448","-14.94432","-4.17751"
"user_002","Standing",1446309439342,"-2.49022","-9.19628","-1.11189"
"user_002","Standing",1446309439349,"-2.41358","-9.15796","-1.22685"
"user_002","Standing",1446309439358,"-2.56686","-9.15796","-1.30349"
"user_002","Standing",1446309439365,"-2.75846","-9.08132","-1.11189"
"user_002","Standing",1446309439373,"-2.75846","-9.08132","-1.15021"
"user_002","Standing",1446309439382,"-2.8351","-9.15796","-0.920286"
"user_002","Standing",1446309439390,"-2.8357","-9.15855","-0.919687"
"user_002","Standing",1446309439398,"-2.95007","-9.2346","-0.881966"
"user_002","Standing",1446309439406,"-2.8351","-9.11964","-0.958607"
"user_002","Standing",1446309439414,"-2.8351","-8.96635","-1.15021"
"user_002","Standing",1446309439422,"-2.95007","-9.08132","-0.920286"
"user_002","Standing",1446309439430,"-2.95007","-8.88971","-0.996927"
"user_002","Standing",1446309439438,"-2.91174","-9.00468","-1.15021"
"user_002","Standing",1446309439447,"-3.02671","-8.96635","-0.996927"
"user_002","Standing",1446309439454,"-2.79678","-8.96635","-1.15021"
"user_002","Standing",1446309439463,"-2.87342","-9.08132","-1.34181"
"user_002","Standing",1446309439471,"-2.98839","-9.19628","-1.22685"
"user_002","Standing",1446309439479,"-2.95007","-9.00468","-1.30349"
"user_002","Standing",1446309439487,"-2.98839","-9.00468","-1.15021"
"user_002","Standing",1446309439495,"-3.06503","-9.00468","-0.958607"
"user_002","Standing",1446309439503,"-3.02671","-9.04299","-0.881966"
"user_002","Standing",1446309439511,"-2.91174","-9.00468","-0.920286"
"user_002","Standing",1446309439519,"-2.95007","-9.08132","-0.767005"
"user_002","Standing",1446309439527,"-2.8351","-9.00468","-0.958607"
"user_002","Standing",1446309439536,"-2.95007","-9.00468","-0.996927"
"user_002","Standing",1446309439543,"-2.75846","-9.04299","-0.690364"
"user_002","Standing",1446309439552,"-2.6435","-9.00468","-1.03525"
"user_002","Standing",1446309439560,"-2.72014","-9.00468","-1.15021"
"user_002","Standing",1446309439568,"-2.68182","-9.04299","-1.11189"
"user_002","Standing",1446309439576,"-2.60518","-9.00468","-1.11189"
"user_002","Standing",1446309439584,"-2.52854","-8.88971","-1.15021"
"user_002","Standing",1446309439593,"-2.6435","-8.92803","-1.03525"
"user_002","Standing",1446309439601,"-2.60518","-8.96635","-0.996927"
"user_002","Standing",1446309439609,"-2.6435","-9.04299","-0.996927"
"user_002","Standing",1446309439616,"-2.75846","-9.04299","-0.920286"
"user_002","Standing",1446309439624,"-2.6435","-9.19628","-0.805325"
"user_002","Standing",1446309439633,"-2.79678","-8.96635","-0.767005"
"user_002","Standing",1446309439641,"-2.87342","-8.92803","-0.958607"
"user_002","Standing",1446309439649,"-2.60518","-9.11964","-0.843646"
"user_002","Standing",1446309439657,"-2.8351","-9.08132","-0.843646"
"user_002","Standing",1446309439665,"-2.8351","-9.2346","-0.920286"
"user_002","Standing",1446309439674,"-2.72014","-9.11964","-0.958607"
"user_002","Standing",1446309439682,"-2.87342","-9.15796","-1.18853"
"user_002","Standing",1446309439690,"-3.06503","-9.2346","-1.18853"
"user_002","Standing",1446309439698,"-2.8351","-9.08132","-0.996927"
"user_002","Standing",1446309439705,"-2.98839","-9.04299","-1.03525"
"user_002","Standing",1446309439713,"-3.17999","-8.96635","-1.18853"
"user_002","Standing",1446309439722,"-3.21831","-8.88971","-1.18853"
"user_002","Standing",1446309439729,"-3.17999","-8.92803","-1.15021"
"user_002","Standing",1446309439738,"-3.17999","-8.77475","-1.22685"
"user_002","Standing",1446309439746,"-3.33327","-8.65979","-1.07357"
"user_002","Standing",1446309439754,"-3.37159","-8.58315","-1.34181"
"user_002","Standing",1446309439762,"-3.33327","-8.77475","-1.18853"
"user_002","Standing",1446309439771,"-3.33327","-8.58315","-1.07357"
"user_002","Standing",1446309439779,"-3.14167","-8.92803","-1.03525"
"user_002","Standing",1446309439787,"-3.25663","-8.85139","-0.881966"
"user_002","Standing",1446309439795,"-3.10335","-8.85139","-0.920286"
"user_002","Standing",1446309439803,"-2.87342","-8.85139","-0.843646"
"user_002","Standing",1446309439811,"-2.91174","-8.92803","-0.767005"
"user_002","Standing",1446309439819,"-2.87342","-8.88971","-0.805325"
"user_002","Standing",1446309439827,"-2.98839","-8.96635","-0.767005"
"user_002","Standing",1446309439835,"-2.79678","-9.11964","-1.07357"
"user_002","Standing",1446309439843,"-2.87342","-9.08132","-0.920286"
"user_002","Standing",1446309439851,"-2.95007","-9.15796","-0.805325"
"user_002","Standing",1446309439859,"-3.02671","-8.85139","-0.728685"
"user_002","Standing",1446309439868,"-2.98839","-8.92803","-0.690364"
"user_002","Standing",1446309439875,"-2.98839","-8.96635","-0.690364"
"user_002","Standing",1446309439883,"-2.91174","-8.96635","-0.881966"
"user_002","Standing",1446309439892,"-3.02671","-8.85139","-0.613724"
"user_002","Standing",1446309439900,"-3.06503","-9.04299","-0.767005"
"user_002","Standing",1446309439908,"-2.87342","-8.73643","-0.652044"
"user_002","Standing",1446309439916,"-2.95007","-8.88971","-0.728685"
"user_002","Standing",1446309439924,"-3.10335","-8.77475","-0.690364"
"user_002","Standing",1446309439932,"-2.91174","-8.77475","-0.652044"
"user_002","Standing",1446309439940,"-2.91174","-9.04299","-0.805325"
"user_002","Standing",1446309439948,"-2.91174","-9.04299","-0.767005"
"user_002","Standing",1446309439957,"-3.02671","-9.04299","-0.652044"
"user_002","Standing",1446309439965,"-3.06503","-9.27292","-0.805325"
"user_002","Standing",1446309439973,"-3.14167","-9.00468","-0.767005"
"user_002","Standing",1446309439980,"-2.95007","-8.96635","-0.843646"
"user_002","Standing",1446309439989,"-3.10335","-9.00468","-1.15021"
"user_002","Standing",1446309439997,"-2.98839","-9.19628","-1.03525"
"user_002","Standing",1446309440004,"-3.10335","-9.19628","-1.15021"
"user_002","Standing",1446309440013,"-2.91174","-9.11964","-1.18853"
"user_002","Standing",1446309440021,"-2.91174","-9.08132","-1.22685"
"user_002","Standing",1446309440029,"-2.95007","-9.00468","-1.26517"
"user_002","Standing",1446309440038,"-3.06503","-9.08132","-1.15021"
"user_002","Standing",1446309440045,"-3.06503","-9.00468","-1.03525"
"user_002","Standing",1446309440054,"-3.10335","-9.11964","-1.07357"
"user_002","Standing",1446309440062,"-3.10335","-8.96635","-0.996927"
"user_002","Standing",1446309440069,"-3.10335","-8.96635","-1.03525"
"user_002","Standing",1446309440078,"-3.17999","-9.00468","-1.11189"
"user_002","Standing",1446309440086,"-3.14167","-8.85139","-0.996927"
"user_002","Standing",1446309440094,"-3.17999","-9.00468","-0.728685"
"user_002","Standing",1446309440102,"-3.17999","-8.96635","-0.958607"
"user_002","Standing",1446309440111,"-3.10335","-9.00468","-0.881966"
"user_002","Standing",1446309440119,"-3.17999","-9.00468","-1.03525"
"user_002","Standing",1446309440126,"-3.02671","-9.00468","-0.881966"
"user_002","Standing",1446309440135,"-3.06503","-9.00468","-0.728685"
"user_002","Standing",1446309440142,"-3.21831","-8.92803","-1.03525"
"user_002","Standing",1446309440151,"-3.33327","-8.85139","-0.767005"
"user_002","Standing",1446309440158,"-3.21831","-9.04299","-0.652044"
"user_002","Standing",1446309440167,"-3.33327","-8.85139","-0.613724"
"user_002","Standing",1446309440175,"-3.37159","-8.85139","-0.345482"
"user_002","Standing",1446309440183,"-3.37159","-9.00468","-0.652044"
"user_002","Standing",1446309440192,"-3.33327","-8.81307","-0.460442"
"user_002","Standing",1446309440199,"-3.21831","-9.08132","-0.537083"
"user_002","Standing",1446309440208,"-3.21831","-8.92803","-0.690364"
"user_002","Standing",1446309440215,"-3.14167","-8.96635","-0.575403"
"user_002","Standing",1446309440224,"-3.17999","-8.92803","-0.690364"
"user_002","Standing",1446309440232,"-3.17999","-8.77475","-0.690364"
"user_002","Standing",1446309440239,"-3.14167","-8.88971","-0.805325"
"user_002","Standing",1446309440248,"-3.10335","-9.04299","-0.843646"
"user_002","Standing",1446309440255,"-3.14167","-8.88971","-0.767005"
"user_002","Standing",1446309440264,"-3.06503","-9.11964","-0.805325"
"user_002","Standing",1446309440272,"-3.14167","-8.96635","-0.690364"
"user_002","Standing",1446309440280,"-3.29495","-9.08132","-0.843646"
"user_002","Standing",1446309440288,"-3.33327","-8.81307","-0.575403"
"user_002","Standing",1446309440296,"-3.21831","-8.88971","-0.575403"
"user_002","Standing",1446309440305,"-3.21831","-8.96635","-0.613724"
"user_002","Standing",1446309440312,"-3.14167","-8.77475","-0.537083"
"user_002","Standing",1446309440320,"-3.10335","-8.85139","-0.613724"
"user_002","Standing",1446309440329,"-3.21831","-9.00468","-0.613724"
"user_002","Standing",1446309440337,"-3.14167","-8.85139","-0.613724"
"user_002","Standing",1446309440345,"-3.21831","-9.04299","-0.690364"
"user_002","Standing",1446309440353,"-3.06503","-8.92803","-0.575403"
"user_002","Standing",1446309440361,"-3.25663","-9.11964","-0.728685"
"user_002","Standing",1446309440369,"-3.21831","-8.92803","-0.652044"
"user_002","Standing",1446309440377,"-3.06503","-8.92803","-0.843646"
"user_002","Standing",1446309440385,"-3.06503","-9.04299","-0.690364"
"user_002","Standing",1446309440394,"-3.21831","-9.00468","-0.460442"
"user_002","Standing",1446309440402,"-3.02671","-8.92803","-0.652044"
"user_002","Standing",1446309440410,"-3.21831","-8.96635","-0.652044"
"user_002","Standing",1446309440417,"-3.25663","-8.96635","-0.767005"
"user_002","Standing",1446309440426,"-3.21831","-8.88971","-0.728685"
"user_002","Standing",1446309440434,"-3.37159","-8.85139","-0.767005"
"user_002","Standing",1446309440443,"-3.21831","-8.85139","-0.537083"
"user_002","Standing",1446309440450,"-3.10335","-9.11964","-0.767005"
"user_002","Standing",1446309440458,"-3.10335","-9.19628","-0.920286"
"user_002","Standing",1446309440467,"-3.10335","-9.00468","-0.767005"
"user_002","Standing",1446309440474,"-3.02671","-8.96635","-0.767005"
"user_002","Standing",1446309440482,"-3.10335","-8.92803","-0.805325"
"user_002","Standing",1446309440491,"-3.17999","-8.92803","-0.843646"
"user_002","Standing",1446309440498,"-3.33327","-8.96635","-0.805325"
"user_002","Standing",1446309440506,"-3.29495","-8.85139","-0.575403"
"user_002","Standing",1446309440515,"-3.21831","-8.88971","-0.728685"
"user_002","Standing",1446309440523,"-3.29495","-8.92803","-0.652044"
"user_002","Standing",1446309440531,"-3.37159","-9.04299","-0.575403"
"user_002","Standing",1446309440539,"-3.33327","-8.92803","-0.613724"
"user_002","Standing",1446309440547,"-3.33327","-8.88971","-0.498763"
"user_002","Standing",1446309440555,"-3.21831","-9.08132","-0.690364"
"user_002","Standing",1446309440564,"-3.06503","-8.88971","-0.652044"
"user_002","Standing",1446309440571,"-3.17999","-8.88971","-0.537083"
"user_002","Standing",1446309440580,"-3.06503","-8.88971","-0.498763"
"user_002","Standing",1446309440587,"-3.10335","-8.85139","-0.575403"
"user_002","Standing",1446309440596,"-3.06503","-9.08132","-0.613724"
"user_002","Standing",1446309440604,"-2.87342","-8.85139","-0.652044"
"user_002","Standing",1446309440612,"-2.95007","-9.08132","-0.728685"
"user_002","Standing",1446309440620,"-3.14167","-8.96635","-0.422122"
"user_002","Standing",1446309440628,"-3.02671","-8.92803","-0.537083"
"user_002","Standing",1446309440636,"-3.14167","-9.00468","-0.422122"
"user_002","Standing",1446309440645,"-3.10335","-9.08132","-0.383802"
"user_002","Standing",1446309440653,"-3.14167","-8.81307","-0.307161"
"user_002","Standing",1446309440660,"-3.17999","-8.85139","-0.422122"
"user_002","Standing",1446309440669,"-3.21831","-8.85139","-0.1922"
"user_002","Standing",1446309440676,"-3.17999","-9.04299","-0.498763"
"user_002","Standing",1446309440685,"-3.02671","-9.04299","-0.460442"
"user_002","Standing",1446309440693,"-3.21831","-8.85139","-0.498763"
"user_002","Standing",1446309440701,"-3.10335","-9.08132","-0.498763"
"user_002","Standing",1446309440709,"-3.29495","-8.96635","-0.537083"
"user_002","Standing",1446309440717,"-3.06503","-8.88971","-0.383802"
"user_002","Standing",1446309440725,"-3.10335","-9.15796","-0.498763"
"user_002","Standing",1446309440734,"-2.91174","-9.00468","-0.345482"
"user_002","Standing",1446309440741,"-3.17999","-8.88971","-0.498763"
"user_002","Standing",1446309440749,"-3.21831","-9.08132","-0.537083"
"user_002","Standing",1446309440757,"-3.06503","-9.00468","-0.460442"
"user_002","Standing",1446309440766,"-3.06503","-9.00468","-0.613724"
"user_002","Standing",1446309440774,"-3.10335","-8.92803","-0.498763"
"user_002","Standing",1446309440782,"-3.25663","-8.92803","-0.613724"
"user_002","Standing",1446309440790,"-3.17999","-8.92803","-0.728685"
"user_002","Standing",1446309440798,"-3.29495","-9.04299","-0.422122"
"user_002","Standing",1446309440806,"-3.17999","-9.08132","-0.422122"
"user_002","Standing",1446309440814,"-3.21831","-9.00468","-0.460442"
"user_002","Standing",1446309440822,"-3.06503","-8.96635","-0.460442"
"user_002","Standing",1446309440831,"-3.17999","-9.04299","-0.537083"
"user_002","Standing",1446309440839,"-3.14167","-9.04299","-0.498763"
"user_002","Standing",1446309440847,"-3.17999","-9.08132","-0.345482"
"user_002","Standing",1446309440855,"-3.21831","-9.08132","-0.613724"
"user_002","Standing",1446309440863,"-3.33327","-9.15796","-0.460442"
"user_002","Standing",1446309440871,"-3.37159","-9.00468","-0.460442"
"user_002","Standing",1446309440879,"-3.17999","-8.92803","-0.537083"
"user_002","Standing",1446309440887,"-3.17999","-8.96635","-0.345482"
"user_002","Standing",1446309440896,"-3.17999","-9.04299","-0.383802"
"user_002","Standing",1446309440904,"-3.37159","-9.11964","-0.345482"
"user_002","Standing",1446309440912,"-3.33327","-9.04299","-0.460442"
"user_002","Standing",1446309440920,"-3.44823","-8.96635","-0.460442"
"user_002","Standing",1446309440927,"-3.25663","-8.81307","-0.345482"
"user_002","Standing",1446309440936,"-3.25663","-8.92803","-0.460442"
"user_002","Standing",1446309440944,"-3.40991","-8.85139","-0.652044"
"user_002","Standing",1446309440951,"-3.21831","-8.85139","-0.575403"
"user_002","Standing",1446309440960,"-3.33327","-8.85139","-0.498763"
"user_002","Standing",1446309440968,"-3.37159","-8.85139","-0.460442"
"user_002","Standing",1446309440976,"-3.17999","-8.81307","-0.728685"
"user_002","Standing",1446309440985,"-2.98839","-8.88971","-0.575403"
"user_002","Standing",1446309440992,"-3.06503","-8.85139","-0.613724"
"user_002","S...

ScaDaMaLe Course site and book

Community Packages in Spark - more generally

Let us recall the following quoate in Chapter 10 of High Performance Spark book (needs access to Orielly publishers via your library/subscription): - https://learning.oreilly.com/library/view/high-performance-spark/9781491943199/ch10.html#components

Beyond the integrated components, the community packages can add important functionality to Spark, sometimes even superseding built-in functionality—like with GraphFrames.

Here we introduce you to GraphFrames quickly so you don't need to drop down to the GraphX library that requires more understanding of caching and checkpointing to keep the vertex program's DAG from exploding or becoming inefficient.

GraphFrames User Guide (Scala)

GraphFrames is a package for Apache Spark which provides DataFrame-based Graphs. It provides high-level APIs in Scala, Java, and Python. It aims to provide both the functionality of GraphX and extended functionality taking advantage of Spark DataFrames. This extended functionality includes motif finding, DataFrame-based serialization, and highly expressive graph queries.

The GraphFrames package is available from Spark Packages.

This notebook demonstrates examples from the GraphFrames User Guide: https://graphframes.github.io/graphframes/docs/_site/user-guide.html.

sc.version // link the right library depending on Spark version of the cluster that's running
// spark version 2.3.0 works with graphframes:graphframes:0.7.0-spark2.3-s_2.11
// spark version 3.0.1 works with graphframes:graphframes:0.8.1-spark3.0-s_2.12
res0: String = 3.1.2

Since databricks.com stopped allowing IFrame embeds we have to open it in a separate window now. The blog is insightful and worth a perusal:

  • https://databricks.com/blog/2016/03/03/introducing-graphframes.html
// we first need to install the library - graphframes as a Spark package - and attach it to our cluster - see note two cells above!
import org.apache.spark.sql._
import org.apache.spark.sql.functions._

import org.graphframes._
import org.apache.spark.sql._
import org.apache.spark.sql.functions._
import org.graphframes._

Creating GraphFrames

Let us try to create an example social network from the blog: * https://databricks.com/blog/2016/03/03/introducing-graphframes.html.

Users can create GraphFrames from vertex and edge DataFrames.

  • Vertex DataFrame: A vertex DataFrame should contain a special column named id which specifies unique IDs for each vertex in the graph.
  • Edge DataFrame: An edge DataFrame should contain two special columns: src (source vertex ID of edge) and dst (destination vertex ID of edge).

Both DataFrames can have arbitrary other columns. Those columns can represent vertex and edge attributes.

In our example, we can use a GraphFrame can store data or properties associated with each vertex and edge.

In our social network, each user might have an age and name, and each connection might have a relationship type.

Create the vertices and edges

// Vertex DataFrame
val v = sqlContext.createDataFrame(List(
  ("a", "Alice", 34),
  ("b", "Bob", 36),
  ("c", "Charlie", 30),
  ("d", "David", 29),
  ("e", "Esther", 32),
  ("f", "Fanny", 36),
  ("g", "Gabby", 60)
)).toDF("id", "name", "age")

// Edge DataFrame
val e = sqlContext.createDataFrame(List(
  ("a", "b", "friend"),
  ("b", "c", "follow"),
  ("c", "b", "follow"),
  ("f", "c", "follow"),
  ("e", "f", "follow"),
  ("e", "d", "friend"),
  ("d", "a", "friend"),
  ("a", "e", "friend")
)).toDF("src", "dst", "relationship")
v: org.apache.spark.sql.DataFrame = [id: string, name: string ... 1 more field]
e: org.apache.spark.sql.DataFrame = [src: string, dst: string ... 1 more field]

Let's create a graph from these vertices and these edges:

val g = GraphFrame(v, e)
g: org.graphframes.GraphFrame = GraphFrame(v:[id: string, name: string ... 1 more field], e:[src: string, dst: string ... 1 more field])

Let's use the d3.graphs to visualise graphs (recall the D3 graphs in wiki-click example). You need the Run Cell below using that cell's Play button's drop-down menu.

Warning: classes defined within packages cannot be redefined without a cluster restart.
Compilation successful.
d3.graphs.help()

Produces a force-directed graph given a collection of edges of the following form:
case class Edge(src: String, dest: String, count: Long)

Usage:
import d3._
graphs.force(
  height = 500,
  width = 500,
  clicks: Dataset[Edge])

import org.apache.spark.sql.functions.lit // import the lit function in sql
val gE= g.edges.select($"src", $"dst".as("dest"), lit(1L).as("count")) // for us the column count is just an edge incidence
import org.apache.spark.sql.functions.lit
gE: org.apache.spark.sql.DataFrame = [src: string, dest: string ... 1 more field]
display(gE)
src dest count
a b 1.0
b c 1.0
c b 1.0
f c 1.0
e f 1.0
e d 1.0
d a 1.0
a e 1.0
d3.graphs.force(
  height = 500,
  width = 500,
  clicks = gE.as[d3.Edge])

// This example graph also comes with the GraphFrames package.
val g0 = examples.Graphs.friends
g0: org.graphframes.GraphFrame = GraphFrame(v:[id: string, name: string ... 1 more field], e:[src: string, dst: string ... 1 more field])
d3.graphs.force( // let us see g0 now in one cell
  height = 500,
  width = 500,
  clicks = g0.edges.select($"src", $"dst".as("dest"), lit(1L).as("count")).as[d3.Edge])

Basic graph and DataFrame queries

GraphFrames provide several simple graph queries, such as node degree.

Also, since GraphFrames represent graphs as pairs of vertex and edge DataFrames, it is easy to make powerful queries directly on the vertex and edge DataFrames. Those DataFrames are made available as vertices and edges fields in the GraphFrame.

Simple queries are simple

GraphFrames make it easy to express queries over graphs. Since GraphFrame vertices and edges are stored as DataFrames, many queries are just DataFrame (or SQL) queries.

display(g.vertices)
id name age
a Alice 34.0
b Bob 36.0
c Charlie 30.0
d David 29.0
e Esther 32.0
f Fanny 36.0
g Gabby 60.0
display(g0.vertices) // this is the same query on the graph loaded as an example from GraphFrame package
id name age
a Alice 34.0
b Bob 36.0
c Charlie 30.0
d David 29.0
e Esther 32.0
f Fanny 36.0
g Gabby 60.0
display(g.edges)
src dst relationship
a b friend
b c follow
c b follow
f c follow
e f follow
e d friend
d a friend
a e friend

The incoming degree of the vertices:

display(g.inDegrees)
id inDegree
c 2.0
d 1.0
e 1.0
b 2.0
f 1.0
a 1.0

The outgoing degree of the vertices:

display(g.outDegrees)
id outDegree
a 2.0
c 1.0
e 2.0
d 1.0
b 1.0
f 1.0

The degree of the vertices:

display(g.degrees)
id degree
b 3.0
a 3.0
c 3.0
f 2.0
e 3.0
d 2.0

You can run queries directly on the vertices DataFrame. For example, we can find the age of the youngest person in the graph:

val youngest = g.vertices.groupBy().min("age")
display(youngest)
min(age)
29.0

Likewise, you can run queries on the edges DataFrame.

For example, let us count the number of 'follow' relationships in the graph:

val numFollows = g.edges.filter("relationship = 'follow'").count()
numFollows: Long = 4

Motif finding

More complex relationships involving edges and vertices can be built using motifs.

The following cell finds the pairs of vertices with edges in both directions between them.

The result is a dataframe, in which the column names are given by the motif keys.

Check out the GraphFrame User Guide at https://graphframes.github.io/graphframes/docs/_site/user-guide.html for more details on the API.

// Search for pairs of vertices with edges in both directions between them, i.e., find undirected or bidirected edges.
val motifs = g.find("(a)-[e1]->(b); (b)-[e2]->(a)")
display(motifs)

Since the result is a DataFrame, more complex queries can be built on top of the motif.

Let us find all the reciprocal relationships in which one person is older than 30:

val filtered = motifs.filter("b.age > 30")
display(filtered)

You Try!

//Search for all "directed triangles" or triplets of vertices: a,b,c with edges: a->b, b->c and c->a
//uncomment the next 2 lines and replace the "XXX" below
//val motifs3 = g.find("(a)-[e1]->(b); (b)-[e2]->(c); (c)-[e3]->(XXX)")
//display(motifs3)

Stateful queries

Many motif queries are stateless and simple to express, as in the examples above. The next examples demonstrate more complex queries which carry state along a path in the motif. These queries can be expressed by combining GraphFrame motif finding with filters on the result, where the filters use sequence operations to construct a series of DataFrame Columns.

For example, suppose one wishes to identify a chain of 4 vertices with some property defined by a sequence of functions. That is, among chains of 4 vertices a->b->c->d, identify the subset of chains matching this complex filter:

  • Initialize state on path.
  • Update state based on vertex a.
  • Update state based on vertex b.
  • Etc. for c and d.
  • If final state matches some condition, then the chain is accepted by the filter.

The below code snippets demonstrate this process, where we identify chains of 4 vertices such that at least 2 of the 3 edges are friend relationships. In this example, the state is the current count of friend edges; in general, it could be any DataFrame Column.

// Find chains of 4 vertices.
val chain4 = g.find("(a)-[ab]->(b); (b)-[bc]->(c); (c)-[cd]->(d)")

// Query on sequence, with state (cnt)
//  (a) Define method for updating state given the next element of the motif.
def sumFriends(cnt: Column, relationship: Column): Column = {
  when(relationship === "friend", cnt + 1).otherwise(cnt)
}
//  (b) Use sequence operation to apply method to sequence of elements in motif.
//      In this case, the elements are the 3 edges.
val condition = Seq("ab", "bc", "cd").
  foldLeft(lit(0))((cnt, e) => sumFriends(cnt, col(e)("relationship")))
//  (c) Apply filter to DataFrame.
val chainWith2Friends2 = chain4.where(condition >= 2)
display(chainWith2Friends2)
chain4
res22: org.apache.spark.sql.DataFrame = [a: struct<id: string, name: string ... 1 more field>, ab: struct<src: string, dst: string ... 1 more field> ... 5 more fields]
chain4.printSchema
root
 |-- a: struct (nullable = false)
 |    |-- id: string (nullable = true)
 |    |-- name: string (nullable = true)
 |    |-- age: integer (nullable = false)
 |-- ab: struct (nullable = false)
 |    |-- src: string (nullable = true)
 |    |-- dst: string (nullable = true)
 |    |-- relationship: string (nullable = true)
 |-- b: struct (nullable = false)
 |    |-- id: string (nullable = true)
 |    |-- name: string (nullable = true)
 |    |-- age: integer (nullable = false)
 |-- bc: struct (nullable = false)
 |    |-- src: string (nullable = true)
 |    |-- dst: string (nullable = true)
 |    |-- relationship: string (nullable = true)
 |-- c: struct (nullable = false)
 |    |-- id: string (nullable = true)
 |    |-- name: string (nullable = true)
 |    |-- age: integer (nullable = false)
 |-- cd: struct (nullable = false)
 |    |-- src: string (nullable = true)
 |    |-- dst: string (nullable = true)
 |    |-- relationship: string (nullable = true)
 |-- d: struct (nullable = false)
 |    |-- id: string (nullable = true)
 |    |-- name: string (nullable = true)
 |    |-- age: integer (nullable = false)

An idea -- a diatribe into an AI security product.

Can you think of a way to use stateful queries in social media networks to find perpetrators of hate-speech online who are possibly worthy of an investigation by domain experts, say in the intelligence or security domain, for potential prosecution on charges of having incited another person to cause physical violence... This is a real problem today as Swedish law effectively prohibits certain forms of online hate-speech.

An idea for a product that can be used by Swedish security agencies?

See https://näthatsgranskaren.se/ for details of a non-profit in Sweden doing such operaitons mostly manually as of early 2020.

Subgraphs

Subgraphs are built by filtering a subset of edges and vertices. For example, the following subgraph only contains people who are friends and who are more than 30 years old.

// Select subgraph of users older than 30, and edges of type "friend"
val v2 = g.vertices.filter("age > 30")
val e2 = g.edges.filter("relationship = 'friend'")
val g2 = GraphFrame(v2, e2)
v2: org.apache.spark.sql.Dataset[org.apache.spark.sql.Row] = [id: string, name: string ... 1 more field]
e2: org.apache.spark.sql.Dataset[org.apache.spark.sql.Row] = [src: string, dst: string ... 1 more field]
g2: org.graphframes.GraphFrame = GraphFrame(v:[id: string, name: string ... 1 more field], e:[src: string, dst: string ... 1 more field])
display(g2.vertices)
id name age
a Alice 34.0
b Bob 36.0
e Esther 32.0
f Fanny 36.0
g Gabby 60.0
display(g2.edges)
src dst relationship
a b friend
e d friend
d a friend
a e friend
d3.graphs.force( // let us see g2 now in one cell
  height = 500,
  width = 500,
  clicks = g2.edges.select($"src", $"dst".as("dest"), lit(1L).as("count")).as[d3.Edge])

Complex triplet filters

The following example shows how to select a subgraph based upon triplet filters which operate on:

  • an edge and
  • its src and
  • dst vertices.

This example could be extended to go beyond triplets by using more complex motifs.

// Select subgraph based on edges "e" of type "follow"
// pointing from a younger user "a" to an older user "b".
val paths = g.find("(a)-[e]->(b)")
  .filter("e.relationship = 'follow'")
  .filter("a.age < b.age")
// "paths" contains vertex info. Extract the edges.
val e2 = paths.select("e.src", "e.dst", "e.relationship")
// In Spark 1.5+, the user may simplify this call:
//  val e2 = paths.select("e.*")

// Construct the subgraph
val g2 = GraphFrame(g.vertices, e2)
paths: org.apache.spark.sql.Dataset[org.apache.spark.sql.Row] = [a: struct<id: string, name: string ... 1 more field>, e: struct<src: string, dst: string ... 1 more field> ... 1 more field]
e2: org.apache.spark.sql.DataFrame = [src: string, dst: string ... 1 more field]
g2: org.graphframes.GraphFrame = GraphFrame(v:[id: string, name: string ... 1 more field], e:[src: string, dst: string ... 1 more field])
display(g2.vertices)
id name age
a Alice 34.0
b Bob 36.0
c Charlie 30.0
d David 29.0
e Esther 32.0
f Fanny 36.0
g Gabby 60.0
display(g2.edges)
src dst relationship
c b follow
e f follow

Standard graph algorithms in GraphX conveniently via GraphFrames

GraphFrames comes with a number of standard graph algorithms built in:

  • Breadth-first search (BFS)
  • Connected components
  • Strongly connected components
  • Label Propagation Algorithm (LPA)
  • PageRank
  • Shortest paths
  • Triangle count

Read

https://graphframes.github.io/graphframes/docs/_site/user-guide.html

Search from "Esther" for users of age < 32.

// Search from "Esther" for users of age <= 32.
val paths: DataFrame = g.bfs.fromExpr("name = 'Esther'").toExpr("age < 32").run()
display(paths)
val paths: DataFrame = g.bfs.fromExpr("name = 'Esther' OR name = 'Bob'").toExpr("age < 32").run()
display(paths)

The search may also be limited by edge filters and maximum path lengths.

val filteredPaths = g.bfs.fromExpr("name = 'Esther'").toExpr("age < 32")
  .edgeFilter("relationship != 'friend'")
  .maxPathLength(3)
  .run()
display(filteredPaths)

Connected components

Compute the connected component membership of each vertex and return a graph with each vertex assigned a component ID.

READ https://graphframes.github.io/graphframes/docs/_site/user-guide.html#connected-components.

From https://graphframes.github.io/graphframes/docs/_site/user-guide.html#connected-components:-

NOTE: With GraphFrames 0.3.0 and later releases, the default Connected Components algorithm requires setting a Spark checkpoint directory. Users can revert to the old algorithm using .setAlgorithm("graphx").

Recall the following quote from Chapter 5 on Effective Transformations of the High Performance Spark Book why one needs to check-point to keep the RDD lineage DAGs from growing too large.

Types of Reuse: Cache, Persist, Checkpoint, Shuffle Files If you decide that you need to reuse your RDD, Spark provides a multitude of options for how to store the RDD. Thus it is important to understand when to use the various types of persistence.There are three primary operations that you can use to store your RDD: cache, persist, and checkpoint. In general, caching (equivalent to persisting with the in-memory storage) and persisting are most useful to avoid recomputation during one Spark job or to break RDDs with long lineages, since they keep an RDD on the executors during a Spark job. Checkpointing is most useful to prevent failures and a high cost of recomputation by saving intermediate results. Like persisting, checkpointing helps avoid computation, thus minimizing the cost of failure, and avoids recomputation by breaking the lineage graph.

sc.setCheckpointDir("/_checkpoint") // just a directory in distributed file system
val result = g.connectedComponents.run() 
display(result)
id name age component
a Alice 34.0 4.12316860416e11
b Bob 36.0 4.12316860416e11
c Charlie 30.0 4.12316860416e11
d David 29.0 4.12316860416e11
e Esther 32.0 4.12316860416e11
f Fanny 36.0 4.12316860416e11
g Gabby 60.0 1.46028888064e11

Fun Exercise: Try to modify the d3.graph function to allow a visualisation of a given Sequence of component ids in the above result.

Strongly connected components

Compute the strongly connected component (SCC) of each vertex and return a graph with each vertex assigned to the SCC containing that vertex.

READ https://graphframes.github.io/graphframes/docs/_site/user-guide.html#strongly-connected-components.

val result = g.stronglyConnectedComponents.maxIter(10).run()
display(result.orderBy("component"))
id name age component
g Gabby 60.0 1.46028888064e11
f Fanny 36.0 4.12316860416e11
a Alice 34.0 6.70014898176e11
e Esther 32.0 6.70014898176e11
d David 29.0 6.70014898176e11
b Bob 36.0 1.047972020224e12
c Charlie 30.0 1.047972020224e12

Label propagation

Run static Label Propagation Algorithm for detecting communities in networks.

Each node in the network is initially assigned to its own community. At every superstep, nodes send their community affiliation to all neighbors and update their state to the mode community affiliation of incoming messages.

LPA is a standard community detection algorithm for graphs. It is very inexpensive computationally, although

  • (1) convergence is not guaranteed and
  • (2) one can end up with trivial solutions (all nodes are identified into a single community).

READ: https://graphframes.github.io/graphframes/docs/_site/user-guide.html#label-propagation-algorithm-lpa.

val result = g.labelPropagation.maxIter(5).run()
display(result.orderBy("label"))
id name age label
g Gabby 60.0 1.46028888064e11
b Bob 36.0 1.047972020224e12
e Esther 32.0 1.382979469312e12
a Alice 34.0 1.382979469312e12
c Charlie 30.0 1.382979469312e12
f Fanny 36.0 1.46028888064e12
d David 29.0 1.46028888064e12

PageRank

Identify important vertices in a graph based on connections.

READ: https://graphframes.github.io/graphframes/docs/_site/user-guide.html#pagerank.

// Run PageRank until convergence to tolerance "tol".
val results = g.pageRank.resetProbability(0.15).tol(0.01).run()
display(results.vertices)
id name age pagerank
b Bob 36.0 2.655507832863289
e Esther 32.0 0.37085233187676075
a Alice 34.0 0.44910633706538744
f Fanny 36.0 0.3283606792049851
g Gabby 60.0 0.1799821386239711
d David 29.0 0.3283606792049851
c Charlie 30.0 2.6878300011606218
display(results.edges)
src dst relationship weight
f c follow 1.0
e f follow 0.5
e d friend 0.5
d a friend 1.0
c b follow 1.0
b c follow 1.0
a e friend 0.5
a b friend 0.5
// Run PageRank for a fixed number of iterations.
val results2 = g.pageRank.resetProbability(0.15).maxIter(10).run()
display(results2.vertices)
id name age pagerank
b Bob 36.0 2.7025217677349773
e Esther 32.0 0.3613490987992571
a Alice 34.0 0.4485115093698443
f Fanny 36.0 0.32504910549694244
g Gabby 60.0 0.17073170731707318
d David 29.0 0.32504910549694244
c Charlie 30.0 2.6667877057849627
// Run PageRank personalized for vertex "a"
val results3 = g.pageRank.resetProbability(0.15).maxIter(10).sourceId("a").run()
display(results3.vertices)
id name age pagerank
b Bob 36.0 0.3366143039702568
e Esther 32.0 7.657840357273027e-2
a Alice 34.0 0.17710831642683564
f Fanny 36.0 3.189213697274781e-2
g Gabby 60.0 0.0
d David 29.0 3.189213697274781e-2
c Charlie 30.0 0.3459147020846817

Shortest paths

Computes shortest paths to the given set of landmark vertices, where landmarks are specified by vertex ID.

READ https://graphframes.github.io/graphframes/docs/_site/user-guide.html#shortest-paths.

val paths = g.shortestPaths.landmarks(Seq("a", "d")).run()
display(paths)
g.edges.show()
+---+---+------------+
|src|dst|relationship|
+---+---+------------+
|  a|  b|      friend|
|  b|  c|      follow|
|  c|  b|      follow|
|  f|  c|      follow|
|  e|  f|      follow|
|  e|  d|      friend|
|  d|  a|      friend|
|  a|  e|      friend|
+---+---+------------+

Triangle count

Computes the number of triangles passing through each vertex.

val results = g.triangleCount.run()
display(results)
count id name age
1.0 a Alice 34.0
0.0 b Bob 36.0
0.0 c Charlie 30.0
1.0 d David 29.0
1.0 e Esther 32.0
0.0 f Fanny 36.0
0.0 g Gabby 60.0

YouTry

Read about https://graphframes.github.io/graphframes/docs/_site/user-guide.html#message-passing-via-aggregatemessages

and undestand how the below code snippet shows how to use aggregateMessages to compute the sum of the ages of adjacent users.

import org.graphframes.{examples,GraphFrame}
import org.graphframes.lib.AggregateMessages
val g: GraphFrame = examples.Graphs.friends  // get example graph

// We will use AggregateMessages utilities later, so name it "AM" for short.
val AM = AggregateMessages

// For each user, sum the ages of the adjacent users.
val msgToSrc = AM.dst("age")
val msgToDst = AM.src("age")
val agg = { g.aggregateMessages
  .sendToSrc(msgToSrc)  // send destination user's age to source
  .sendToDst(msgToDst)  // send source user's age to destination
  .agg(sum(AM.msg).as("summedAges")) } // sum up ages, stored in AM.msg column
agg.show()
+---+----------+
| id|summedAges|
+---+----------+
|  a|        97|
|  c|       108|
|  e|        99|
|  d|        66|
|  b|        94|
|  f|        62|
+---+----------+

import org.graphframes.{examples, GraphFrame}
import org.graphframes.lib.AggregateMessages
g: org.graphframes.GraphFrame = GraphFrame(v:[id: string, name: string ... 1 more field], e:[src: string, dst: string ... 1 more field])
AM: org.graphframes.lib.AggregateMessages.type = org.graphframes.lib.AggregateMessages$@706833c8
msgToSrc: org.apache.spark.sql.Column = dst[age]
msgToDst: org.apache.spark.sql.Column = src[age]
agg: org.apache.spark.sql.DataFrame = [id: string, summedAges: bigint]

There is a lot more that can be done with aggregate messaging - let's get into belief propogation algorithm for a more complex example!

Belief propogation is a powerful computational framework for Graphical Models.

as

This provides a template for building customized BP algorithms for different types of graphical models.

Project Idea

Understand parallel belief propagation using colored fields in the Scala code linked above and also pasted below in one cell (for you to modify if you want to do it in a databricks or jupyter or zeppelin notebook) unless you want to fork and extend the github repo directly with your own example.

Then use it with necessary adaptations to be able to model your favorite interacting particle system. Don't just redo the Ising model done there!

This can be used to gain intuition for various real-world scenarios, including the mathematics in your head:

  • Make a graph for contact network of a set of hosts
  • A simple model of COVID spreading in an SI or SIS or SIR or other epidemic models
    • this can be abstract and simply show your skills in programming, say create a random network
    • or be more explicit with some assumptions about the contact process (population sampled, in one or two cities, with some assumptions on contacts during transportation, school, work, etc)
    • show that you have a fully scalable simulation model that can theoretically scale to billions of hosts

The project does not have to be a recommendation to Swedish authorities! Just a start in the right direction, for instance.

Some readings that can help here include the following and references therein:

  • The Transmission Process: A Combinatorial Stochastic Process for the Evolution of Transmission Trees over Networks, Raazesh Sainudiin and David Welch, Journal of Theoretical Biology, Volume 410, Pages 137–170, 10.1016/j.jtbi.2016.07.038, 2016.

Other Project Ideas

  • try to do a scalable inference algorithm for one of the graphical models that you already know...
  • make a large simulaiton of your favourite Finite Markov Information Exchange (FMIE) process defined by Aldous (see reference in the above linked paper)
  • anything else that fancies you or your research orientation/interests and can benefit from adapting the template for the parallel belief propagation algorithm here.

If you want to do this project in databricks (or other) notebook then start by modifying the following code from the example and making it run... Then adapt... start in small steps... make a team with fellow students with complementary skills...

/*
 * Licensed to the Apache Software Foundation (ASF) under one or more
 * contributor license agreements.  See the NOTICE file distributed with
 * this work for additional information regarding copyright ownership.
 * The ASF licenses this file to You under the Apache License, Version 2.0
 * (the "License"); you may not use this file except in compliance with
 * the License.  You may obtain a copy of the License at
 *
 *    http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */

package org.graphframes.examples

import org.apache.spark.{SparkConf, SparkContext}
import org.apache.spark.graphx.{Graph, VertexRDD, Edge => GXEdge}
import org.apache.spark.sql.{Column, Row, SparkSession, SQLContext}
import org.apache.spark.sql.functions.{col, lit, sum, udf, when}

import org.graphframes.GraphFrame
import org.graphframes.examples.Graphs.gridIsingModel
import org.graphframes.lib.AggregateMessages


/**
 * Example code for Belief Propagation (BP)
 *
 * This provides a template for building customized BP algorithms for different types of
 * graphical models.
 *
 * This example:
 *  - Ising model on a grid
 *  - Parallel Belief Propagation using colored fields
 *
 * Ising models are probabilistic graphical models over binary variables x,,i,,.
 * Each binary variable x,,i,, corresponds to one vertex, and it may take values -1 or +1.
 * The probability distribution P(X) (over all x,,i,,) is parameterized by vertex factors a,,i,,
 * and edge factors b,,ij,,:
 * {{{
 *  P(X) = (1/Z) * exp[ \sum_i a_i x_i + \sum_{ij} b_{ij} x_i x_j ]
 * }}}
 * where Z is the normalization constant (partition function).
 * See [[https://en.wikipedia.org/wiki/Ising_model Wikipedia]] for more information on Ising models.
 *
 * Belief Propagation (BP) provides marginal probabilities of the values of the variables x,,i,,,
 * i.e., P(x,,i,,) for each i.  This allows a user to understand likely values of variables.
 * See [[https://en.wikipedia.org/wiki/Belief_propagation Wikipedia]] for more information on BP.
 *
 * We use a batch synchronous BP algorithm, where batches of vertices are updated synchronously.
 * We follow the mean field update algorithm in Slide 13 of the
 * [[http://www.eecs.berkeley.edu/~wainwrig/Talks/A_GraphModel_Tutorial  talk slides]] from:
 *  Wainwright. "Graphical models, message-passing algorithms, and convex optimization."
 *
 * The batches are chosen according to a coloring.  For background on graph colorings for inference,
 * see for example:
 *  Gonzalez et al. "Parallel Gibbs Sampling: From Colored Fields to Thin Junction Trees."
 *  AISTATS, 2011.
 *
 * The BP algorithm works by:
 *  - Coloring the graph by assigning a color to each vertex such that no neighboring vertices
 *    share the same color.
 *  - In each step of BP, update all vertices of a single color.  Alternate colors.
 */
object BeliefPropagation {

  def main(args: Array[String]): Unit = {
    val spark = SparkSession
      .builder()
      .appName("BeliefPropagation example")
      .getOrCreate()

    val sql = spark.sqlContext

    // Create graphical model g of size 3 x 3.
    val g = gridIsingModel(sql, 3)

    println("Original Ising model:")
    g.vertices.show()
    g.edges.show()

    // Run BP for 5 iterations.
    val numIter = 5
    val results = runBPwithGraphX(g, numIter)

    // Display beliefs.
    val beliefs = results.vertices.select("id", "belief")
    println(s"Done with BP. Final beliefs after $numIter iterations:")
    beliefs.show()

    spark.stop()
  }

  /**
   * Given a GraphFrame, choose colors for each vertex.  No neighboring vertices will share the
   * same color.  The number of colors is minimized.
   *
   * This is written specifically for grid graphs. For non-grid graphs, it should be generalized,
   * such as by using a greedy coloring scheme.
   *
   * @param g  Grid graph generated by [[org.graphframes.examples.Graphs.gridIsingModel()]]
   * @return  Same graph, but with a new vertex column "color" of type Int (0 or 1)
   */
  private def colorGraph(g: GraphFrame): GraphFrame = {
    val colorUDF = udf { (i: Int, j: Int) => (i + j) % 2 }
    val v = g.vertices.withColumn("color", colorUDF(col("i"), col("j")))
    GraphFrame(v, g.edges)
  }

  /**
   * Run Belief Propagation.
   *
   * This implementation of BP shows how to use GraphX's aggregateMessages method.
   * It is simple to convert to and from GraphX format.  This method does the following:
   *  - Color GraphFrame vertices for BP scheduling.
   *  - Convert GraphFrame to GraphX format.
   *  - Run BP using GraphX's aggregateMessages API.
   *  - Augment the original GraphFrame with the BP results (vertex beliefs).
   *
   * @param g  Graphical model created by `org.graphframes.examples.Graphs.gridIsingModel()`
   * @param numIter  Number of iterations of BP to run.  One iteration includes updating each
   *                 vertex's belief once.
   * @return  Same graphical model, but with [[GraphFrame.vertices]] augmented with a new column
   *          "belief" containing P(x,,i,, = +1), the marginal probability of vertex i taking
   *          value +1 instead of -1.
   */
  def runBPwithGraphX(g: GraphFrame, numIter: Int): GraphFrame = {
    // Choose colors for vertices for BP scheduling.
    val colorG = colorGraph(g)
    val numColors: Int = colorG.vertices.select("color").distinct.count().toInt

    // Convert GraphFrame to GraphX, and initialize beliefs.
    val gx0 = colorG.toGraphX
    // Schema maps for extracting attributes
    val vColsMap = colorG.vertexColumnMap
    val eColsMap = colorG.edgeColumnMap
    // Convert vertex attributes to nice case classes.
    val gx1: Graph[VertexAttr, Row] = gx0.mapVertices { case (_, attr) =>
      // Initialize belief at 0.0
      VertexAttr(attr.getDouble(vColsMap("a")), 0.0, attr.getInt(vColsMap("color")))
    }
    // Convert edge attributes to nice case classes.
    val extractEdgeAttr: (GXEdge[Row] => EdgeAttr) = { e =>
      EdgeAttr(e.attr.getDouble(eColsMap("b")))
    }
    var gx: Graph[VertexAttr, EdgeAttr] = gx1.mapEdges(extractEdgeAttr)

    // Run BP for numIter iterations.
    for (iter <- Range(0, numIter)) {
      // For each color, have that color receive messages from neighbors.
      for (color <- Range(0, numColors)) {
        // Send messages to vertices of the current color.
        val msgs: VertexRDD[Double] = gx.aggregateMessages(
          ctx =>
            // Can send to source or destination since edges are treated as undirected.
            if (ctx.dstAttr.color == color) {
              val msg = ctx.attr.b * ctx.srcAttr.belief
              // Only send message if non-zero.
              if (msg != 0) ctx.sendToDst(msg)
            } else if (ctx.srcAttr.color == color) {
              val msg = ctx.attr.b * ctx.dstAttr.belief
              // Only send message if non-zero.
              if (msg != 0) ctx.sendToSrc(msg)
            },
          _ + _)
        // Receive messages, and update beliefs for vertices of the current color.
        gx = gx.outerJoinVertices(msgs) {
          case (vID, vAttr, optMsg) =>
            if (vAttr.color == color) {
              val x = vAttr.a + optMsg.getOrElse(0.0)
              val newBelief = math.exp(-log1pExp(-x))
              VertexAttr(vAttr.a, newBelief, color)
            } else {
              vAttr
            }
        }
      }
    }

    // Convert back to GraphFrame with a new column "belief" for vertices DataFrame.
    val gxFinal: Graph[Double, Unit] = gx.mapVertices((_, attr) => attr.belief).mapEdges(_ => ())
    GraphFrame.fromGraphX(colorG, gxFinal, vertexNames = Seq("belief"))
  }

  case class VertexAttr(a: Double, belief: Double, color: Int)

  case class EdgeAttr(b: Double)

  /**
   * Run Belief Propagation.
   *
   * This implementation of BP shows how to use GraphFrame's aggregateMessages method.
   *  - Color GraphFrame vertices for BP scheduling.
   *  - Run BP using GraphFrame's aggregateMessages API.
   *  - Augment the original GraphFrame with the BP results (vertex beliefs).
   *
   * @param g  Graphical model created by `org.graphframes.examples.Graphs.gridIsingModel()`
   * @param numIter  Number of iterations of BP to run.  One iteration includes updating each
   *                 vertex's belief once.
   * @return  Same graphical model, but with [[GraphFrame.vertices]] augmented with a new column
   *          "belief" containing P(x,,i,, = +1), the marginal probability of vertex i taking
   *          value +1 instead of -1.
   */
  def runBPwithGraphFrames(g: GraphFrame, numIter: Int): GraphFrame = {
    // Choose colors for vertices for BP scheduling.
    val colorG = colorGraph(g)
    val numColors: Int = colorG.vertices.select("color").distinct.count().toInt

    // TODO: Handle vertices without any edges.

    // Initialize vertex beliefs at 0.0.
    var gx = GraphFrame(colorG.vertices.withColumn("belief", lit(0.0)), colorG.edges)

    // Run BP for numIter iterations.
    for (iter <- Range(0, numIter)) {
      // For each color, have that color receive messages from neighbors.
      for (color <- Range(0, numColors)) {
        // Define "AM" for shorthand for referring to the src, dst, edge, and msg fields.
        // (See usage below.)
        val AM = AggregateMessages
        // Send messages to vertices of the current color.
        // We may send to source or destination since edges are treated as undirected.
        val msgForSrc: Column = when(AM.src("color") === color, AM.edge("b") * AM.dst("belief"))
        val msgForDst: Column = when(AM.dst("color") === color, AM.edge("b") * AM.src("belief"))
        val logistic = udf { (x: Double) => math.exp(-log1pExp(-x)) }
        val aggregates = gx.aggregateMessages
          .sendToSrc(msgForSrc)
          .sendToDst(msgForDst)
          .agg(sum(AM.msg).as("aggMess"))
        val v = gx.vertices
        // Receive messages, and update beliefs for vertices of the current color.
        val newBeliefCol = when(v("color") === color && aggregates("aggMess").isNotNull,
          logistic(aggregates("aggMess") + v("a")))
          .otherwise(v("belief"))  // keep old beliefs for other colors
        val newVertices = v
          .join(aggregates, v("id") === aggregates("id"), "left_outer")  // join messages, vertices
          .drop(aggregates("id"))  // drop duplicate ID column (from outer join)
          .withColumn("newBelief", newBeliefCol)  // compute new beliefs
          .drop("aggMess")  // drop messages
          .drop("belief")  // drop old beliefs
          .withColumnRenamed("newBelief", "belief")
        // Cache new vertices using workaround for SPARK-13346
        val cachedNewVertices = AM.getCachedDataFrame(newVertices)
        gx = GraphFrame(cachedNewVertices, gx.edges)
      }
    }

    // Drop the "color" column from vertices
    GraphFrame(gx.vertices.drop("color"), gx.edges)
  }

  /** More numerically stable `log(1 + exp(x))` */
  private def log1pExp(x: Double): Double = {
    if (x > 0) {
      x + math.log1p(math.exp(-x))
    } else {
      math.log1p(math.exp(x))
    }
  }
}

ScaDaMaLe Course site and book

This is a scala version of the python notebook in the following talk:

Homework:

See https://www.brighttalk.com/webcast/12891/199003 (you need to subscribe freely to Bright Talk first). Then go through this scala version of the notebook from the talk.

On-Time Flight Performance with GraphFrames for Apache Spark

This notebook provides an analysis of On-Time Flight Performance and Departure Delays data using GraphFrames for Apache Spark.

Source Data:

References:

Preparation

Extract the Airports and Departure Delays information from S3 / DBFS

// Set File Paths
val tripdelaysFilePath = "/databricks-datasets/flights/departuredelays.csv"
val airportsnaFilePath = "/databricks-datasets/flights/airport-codes-na.txt"
tripdelaysFilePath: String = /databricks-datasets/flights/departuredelays.csv
airportsnaFilePath: String = /databricks-datasets/flights/airport-codes-na.txt
// Obtain airports dataset
// Note that "spark-csv" package is built-in datasource in Spark 2.0
val airportsna = sqlContext.read.format("com.databricks.spark.csv").
  option("header", "true").
  option("inferschema", "true").
  option("delimiter", "\t").
  load(airportsnaFilePath)

airportsna.createOrReplaceTempView("airports_na")

// Obtain departure Delays data
val departureDelays = sqlContext.read.format("com.databricks.spark.csv").option("header", "true").load(tripdelaysFilePath)
departureDelays.createOrReplaceTempView("departureDelays")
departureDelays.cache()

// Available IATA (International Air Transport Association) codes from the departuredelays sample dataset
val tripIATA = sqlContext.sql("select distinct iata from (select distinct origin as iata from departureDelays union all select distinct destination as iata from departureDelays) a")
tripIATA.createOrReplaceTempView("tripIATA")

// Only include airports with atleast one trip from the departureDelays dataset
val airports = sqlContext.sql("select f.IATA, f.City, f.State, f.Country from airports_na f join tripIATA t on t.IATA = f.IATA")
airports.createOrReplaceTempView("airports")
airports.cache()
airportsna: org.apache.spark.sql.DataFrame = [City: string, State: string ... 2 more fields]
departureDelays: org.apache.spark.sql.DataFrame = [date: string, delay: string ... 3 more fields]
tripIATA: org.apache.spark.sql.DataFrame = [iata: string]
airports: org.apache.spark.sql.DataFrame = [IATA: string, City: string ... 2 more fields]
res0: airports.type = [IATA: string, City: string ... 2 more fields]
// Build `departureDelays_geo` DataFrame
// Obtain key attributes such as Date of flight, delays, distance, and airport information (Origin, Destination)  
val departureDelays_geo = sqlContext.sql("select cast(f.date as int) as tripid, cast(concat(concat(concat(concat(concat(concat('2014-', concat(concat(substr(cast(f.date as string), 1, 2), '-')), substr(cast(f.date as string), 3, 2)), ' '), substr(cast(f.date as string), 5, 2)), ':'), substr(cast(f.date as string), 7, 2)), ':00') as timestamp) as `localdate`, cast(f.delay as int), cast(f.distance as int), f.origin as src, f.destination as dst, o.city as city_src, d.city as city_dst, o.state as state_src, d.state as state_dst from departuredelays f join airports o on o.iata = f.origin join airports d on d.iata = f.destination") 

// RegisterTempTable
departureDelays_geo.createOrReplaceTempView("departureDelays_geo")

// Cache and Count
departureDelays_geo.cache()
departureDelays_geo.count()
departureDelays_geo: org.apache.spark.sql.DataFrame = [tripid: int, localdate: timestamp ... 8 more fields]
res2: Long = 1361141
display(departureDelays_geo)
tripid localdate delay distance src dst city_src city_dst state_src state_dst
1011111.0 2014-01-01T11:11:00.000+0000 -5.0 221.0 MSP INL Minneapolis International Falls MN MN
1021111.0 2014-01-02T11:11:00.000+0000 7.0 221.0 MSP INL Minneapolis International Falls MN MN
1031111.0 2014-01-03T11:11:00.000+0000 0.0 221.0 MSP INL Minneapolis International Falls MN MN
1041925.0 2014-01-04T19:25:00.000+0000 0.0 221.0 MSP INL Minneapolis International Falls MN MN
1061115.0 2014-01-06T11:15:00.000+0000 33.0 221.0 MSP INL Minneapolis International Falls MN MN
1071115.0 2014-01-07T11:15:00.000+0000 23.0 221.0 MSP INL Minneapolis International Falls MN MN
1081115.0 2014-01-08T11:15:00.000+0000 -9.0 221.0 MSP INL Minneapolis International Falls MN MN
1091115.0 2014-01-09T11:15:00.000+0000 11.0 221.0 MSP INL Minneapolis International Falls MN MN
1101115.0 2014-01-10T11:15:00.000+0000 -3.0 221.0 MSP INL Minneapolis International Falls MN MN
1112015.0 2014-01-11T20:15:00.000+0000 -7.0 221.0 MSP INL Minneapolis International Falls MN MN
1121925.0 2014-01-12T19:25:00.000+0000 -5.0 221.0 MSP INL Minneapolis International Falls MN MN
1131115.0 2014-01-13T11:15:00.000+0000 -3.0 221.0 MSP INL Minneapolis International Falls MN MN
1141115.0 2014-01-14T11:15:00.000+0000 -6.0 221.0 MSP INL Minneapolis International Falls MN MN
1151115.0 2014-01-15T11:15:00.000+0000 -7.0 221.0 MSP INL Minneapolis International Falls MN MN
1161115.0 2014-01-16T11:15:00.000+0000 -3.0 221.0 MSP INL Minneapolis International Falls MN MN
1171115.0 2014-01-17T11:15:00.000+0000 4.0 221.0 MSP INL Minneapolis International Falls MN MN
1182015.0 2014-01-18T20:15:00.000+0000 -5.0 221.0 MSP INL Minneapolis International Falls MN MN
1191925.0 2014-01-19T19:25:00.000+0000 -7.0 221.0 MSP INL Minneapolis International Falls MN MN
1201115.0 2014-01-20T11:15:00.000+0000 -6.0 221.0 MSP INL Minneapolis International Falls MN MN
1211115.0 2014-01-21T11:15:00.000+0000 0.0 221.0 MSP INL Minneapolis International Falls MN MN
1221115.0 2014-01-22T11:15:00.000+0000 -4.0 221.0 MSP INL Minneapolis International Falls MN MN
1231115.0 2014-01-23T11:15:00.000+0000 -4.0 221.0 MSP INL Minneapolis International Falls MN MN
1241115.0 2014-01-24T11:15:00.000+0000 -3.0 221.0 MSP INL Minneapolis International Falls MN MN
1252015.0 2014-01-25T20:15:00.000+0000 -12.0 221.0 MSP INL Minneapolis International Falls MN MN
1261925.0 2014-01-26T19:25:00.000+0000 -5.0 221.0 MSP INL Minneapolis International Falls MN MN
1271115.0 2014-01-27T11:15:00.000+0000 0.0 221.0 MSP INL Minneapolis International Falls MN MN
1281115.0 2014-01-28T11:15:00.000+0000 -8.0 221.0 MSP INL Minneapolis International Falls MN MN
1291115.0 2014-01-29T11:15:00.000+0000 -2.0 221.0 MSP INL Minneapolis International Falls MN MN
1301115.0 2014-01-30T11:15:00.000+0000 0.0 221.0 MSP INL Minneapolis International Falls MN MN
1311115.0 2014-01-31T11:15:00.000+0000 -3.0 221.0 MSP INL Minneapolis International Falls MN MN
2012015.0 2014-02-01T20:15:00.000+0000 -4.0 221.0 MSP INL Minneapolis International Falls MN MN
2022015.0 2014-02-02T20:15:00.000+0000 0.0 221.0 MSP INL Minneapolis International Falls MN MN
2031115.0 2014-02-03T11:15:00.000+0000 -7.0 221.0 MSP INL Minneapolis International Falls MN MN
2041115.0 2014-02-04T11:15:00.000+0000 -6.0 221.0 MSP INL Minneapolis International Falls MN MN
2051115.0 2014-02-05T11:15:00.000+0000 -4.0 221.0 MSP INL Minneapolis International Falls MN MN
2061115.0 2014-02-06T11:15:00.000+0000 -2.0 221.0 MSP INL Minneapolis International Falls MN MN
2071115.0 2014-02-07T11:15:00.000+0000 -15.0 221.0 MSP INL Minneapolis International Falls MN MN
2082015.0 2014-02-08T20:15:00.000+0000 -4.0 221.0 MSP INL Minneapolis International Falls MN MN
2091925.0 2014-02-09T19:25:00.000+0000 1.0 221.0 MSP INL Minneapolis International Falls MN MN
2101115.0 2014-02-10T11:15:00.000+0000 -3.0 221.0 MSP INL Minneapolis International Falls MN MN
2111115.0 2014-02-11T11:15:00.000+0000 -7.0 221.0 MSP INL Minneapolis International Falls MN MN
2121115.0 2014-02-12T11:15:00.000+0000 -2.0 221.0 MSP INL Minneapolis International Falls MN MN
2131115.0 2014-02-13T11:15:00.000+0000 -3.0 221.0 MSP INL Minneapolis International Falls MN MN
2141115.0 2014-02-14T11:15:00.000+0000 -11.0 221.0 MSP INL Minneapolis International Falls MN MN
2152015.0 2014-02-15T20:15:00.000+0000 16.0 221.0 MSP INL Minneapolis International Falls MN MN
2161925.0 2014-02-16T19:25:00.000+0000 169.0 221.0 MSP INL Minneapolis International Falls MN MN
2171115.0 2014-02-17T11:15:00.000+0000 27.0 221.0 MSP INL Minneapolis International Falls MN MN
2181115.0 2014-02-18T11:15:00.000+0000 96.0 221.0 MSP INL Minneapolis International Falls MN MN
2191115.0 2014-02-19T11:15:00.000+0000 -9.0 221.0 MSP INL Minneapolis International Falls MN MN
2201115.0 2014-02-20T11:15:00.000+0000 -6.0 221.0 MSP INL Minneapolis International Falls MN MN
2211115.0 2014-02-21T11:15:00.000+0000 -4.0 221.0 MSP INL Minneapolis International Falls MN MN
2222015.0 2014-02-22T20:15:00.000+0000 -4.0 221.0 MSP INL Minneapolis International Falls MN MN
2231925.0 2014-02-23T19:25:00.000+0000 -3.0 221.0 MSP INL Minneapolis International Falls MN MN
2241115.0 2014-02-24T11:15:00.000+0000 -2.0 221.0 MSP INL Minneapolis International Falls MN MN
2251115.0 2014-02-25T11:15:00.000+0000 -6.0 221.0 MSP INL Minneapolis International Falls MN MN
2261115.0 2014-02-26T11:15:00.000+0000 -8.0 221.0 MSP INL Minneapolis International Falls MN MN
2271115.0 2014-02-27T11:15:00.000+0000 -8.0 221.0 MSP INL Minneapolis International Falls MN MN
2281115.0 2014-02-28T11:15:00.000+0000 5.0 221.0 MSP INL Minneapolis International Falls MN MN
3012015.0 2014-03-01T20:15:00.000+0000 -4.0 221.0 MSP INL Minneapolis International Falls MN MN
3022000.0 2014-03-02T20:00:00.000+0000 0.0 221.0 MSP INL Minneapolis International Falls MN MN
3031115.0 2014-03-03T11:15:00.000+0000 17.0 221.0 MSP INL Minneapolis International Falls MN MN
3041115.0 2014-03-04T11:15:00.000+0000 0.0 221.0 MSP INL Minneapolis International Falls MN MN
3051115.0 2014-03-05T11:15:00.000+0000 -7.0 221.0 MSP INL Minneapolis International Falls MN MN
3061115.0 2014-03-06T11:15:00.000+0000 -8.0 221.0 MSP INL Minneapolis International Falls MN MN
3071115.0 2014-03-07T11:15:00.000+0000 -10.0 221.0 MSP INL Minneapolis International Falls MN MN
3082000.0 2014-03-08T20:00:00.000+0000 -11.0 221.0 MSP INL Minneapolis International Falls MN MN
3092000.0 2014-03-09T20:00:00.000+0000 -9.0 221.0 MSP INL Minneapolis International Falls MN MN
3101115.0 2014-03-10T11:15:00.000+0000 -10.0 221.0 MSP INL Minneapolis International Falls MN MN
3111115.0 2014-03-11T11:15:00.000+0000 -8.0 221.0 MSP INL Minneapolis International Falls MN MN
3121115.0 2014-03-12T11:15:00.000+0000 -6.0 221.0 MSP INL Minneapolis International Falls MN MN
3131115.0 2014-03-13T11:15:00.000+0000 -8.0 221.0 MSP INL Minneapolis International Falls MN MN
3141115.0 2014-03-14T11:15:00.000+0000 -5.0 221.0 MSP INL Minneapolis International Falls MN MN
3152000.0 2014-03-15T20:00:00.000+0000 -11.0 221.0 MSP INL Minneapolis International Falls MN MN
3162000.0 2014-03-16T20:00:00.000+0000 -10.0 221.0 MSP INL Minneapolis International Falls MN MN
3171115.0 2014-03-17T11:15:00.000+0000 25.0 221.0 MSP INL Minneapolis International Falls MN MN
3181115.0 2014-03-18T11:15:00.000+0000 2.0 221.0 MSP INL Minneapolis International Falls MN MN
3191115.0 2014-03-19T11:15:00.000+0000 -5.0 221.0 MSP INL Minneapolis International Falls MN MN
3201115.0 2014-03-20T11:15:00.000+0000 -6.0 221.0 MSP INL Minneapolis International Falls MN MN
3211115.0 2014-03-21T11:15:00.000+0000 0.0 221.0 MSP INL Minneapolis International Falls MN MN
3222000.0 2014-03-22T20:00:00.000+0000 -10.0 221.0 MSP INL Minneapolis International Falls MN MN
3232000.0 2014-03-23T20:00:00.000+0000 -9.0 221.0 MSP INL Minneapolis International Falls MN MN
3241115.0 2014-03-24T11:15:00.000+0000 -9.0 221.0 MSP INL Minneapolis International Falls MN MN
3251115.0 2014-03-25T11:15:00.000+0000 -4.0 221.0 MSP INL Minneapolis International Falls MN MN
3261115.0 2014-03-26T11:15:00.000+0000 -5.0 221.0 MSP INL Minneapolis International Falls MN MN
3271115.0 2014-03-27T11:15:00.000+0000 9.0 221.0 MSP INL Minneapolis International Falls MN MN
3281115.0 2014-03-28T11:15:00.000+0000 -7.0 221.0 MSP INL Minneapolis International Falls MN MN
3292000.0 2014-03-29T20:00:00.000+0000 -19.0 221.0 MSP INL Minneapolis International Falls MN MN
3302000.0 2014-03-30T20:00:00.000+0000 -10.0 221.0 MSP INL Minneapolis International Falls MN MN
3311115.0 2014-03-31T11:15:00.000+0000 -8.0 221.0 MSP INL Minneapolis International Falls MN MN
2011230.0 2014-02-01T12:30:00.000+0000 -3.0 1014.0 EWR MSY Newark New Orleans NJ LA
2010719.0 2014-02-01T07:19:00.000+0000 -2.0 1014.0 EWR MSY Newark New Orleans NJ LA
2021230.0 2014-02-02T12:30:00.000+0000 -10.0 1014.0 EWR MSY Newark New Orleans NJ LA
2020709.0 2014-02-02T07:09:00.000+0000 59.0 1014.0 EWR MSY Newark New Orleans NJ LA
2021654.0 2014-02-02T16:54:00.000+0000 21.0 1014.0 EWR MSY Newark New Orleans NJ LA
2030719.0 2014-02-03T07:19:00.000+0000 -6.0 1014.0 EWR MSY Newark New Orleans NJ LA
2031659.0 2014-02-03T16:59:00.000+0000 0.0 1014.0 EWR MSY Newark New Orleans NJ LA
2031230.0 2014-02-03T12:30:00.000+0000 0.0 1014.0 EWR MSY Newark New Orleans NJ LA
2032043.0 2014-02-03T20:43:00.000+0000 0.0 1014.0 EWR MSY Newark New Orleans NJ LA
2041230.0 2014-02-04T12:30:00.000+0000 24.0 1014.0 EWR MSY Newark New Orleans NJ LA
2040719.0 2014-02-04T07:19:00.000+0000 168.0 1014.0 EWR MSY Newark New Orleans NJ LA
2041730.0 2014-02-04T17:30:00.000+0000 88.0 1014.0 EWR MSY Newark New Orleans NJ LA
2042043.0 2014-02-04T20:43:00.000+0000 106.0 1014.0 EWR MSY Newark New Orleans NJ LA
2051659.0 2014-02-05T16:59:00.000+0000 0.0 1014.0 EWR MSY Newark New Orleans NJ LA
2050719.0 2014-02-05T07:19:00.000+0000 0.0 1014.0 EWR MSY Newark New Orleans NJ LA
2050929.0 2014-02-05T09:29:00.000+0000 0.0 1014.0 EWR MSY Newark New Orleans NJ LA
2052043.0 2014-02-05T20:43:00.000+0000 46.0 1014.0 EWR MSY Newark New Orleans NJ LA
2060719.0 2014-02-06T07:19:00.000+0000 -3.0 1014.0 EWR MSY Newark New Orleans NJ LA
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2021650.0 2014-02-02T16:50:00.000+0000 77.0 409.0 BNA MSY Nashville New Orleans TN LA
2031240.0 2014-02-03T12:40:00.000+0000 30.0 409.0 BNA MSY Nashville New Orleans TN LA
2031455.0 2014-02-03T14:55:00.000+0000 10.0 409.0 BNA MSY Nashville New Orleans TN LA
2030850.0 2014-02-03T08:50:00.000+0000 -1.0 409.0 BNA MSY Nashville New Orleans TN LA
2031735.0 2014-02-03T17:35:00.000+0000 -3.0 409.0 BNA MSY Nashville New Orleans TN LA
2041240.0 2014-02-04T12:40:00.000+0000 56.0 409.0 BNA MSY Nashville New Orleans TN LA
2041455.0 2014-02-04T14:55:00.000+0000 23.0 409.0 BNA MSY Nashville New Orleans TN LA
2040850.0 2014-02-04T08:50:00.000+0000 -1.0 409.0 BNA MSY Nashville New Orleans TN LA
2041735.0 2014-02-04T17:35:00.000+0000 3.0 409.0 BNA MSY Nashville New Orleans TN LA
2051240.0 2014-02-05T12:40:00.000+0000 33.0 409.0 BNA MSY Nashville New Orleans TN LA
2051455.0 2014-02-05T14:55:00.000+0000 14.0 409.0 BNA MSY Nashville New Orleans TN LA
2050850.0 2014-02-05T08:50:00.000+0000 19.0 409.0 BNA MSY Nashville New Orleans TN LA
2051735.0 2014-02-05T17:35:00.000+0000 26.0 409.0 BNA MSY Nashville New Orleans TN LA
2061240.0 2014-02-06T12:40:00.000+0000 43.0 409.0 BNA MSY Nashville New Orleans TN LA
2061455.0 2014-02-06T14:55:00.000+0000 -2.0 409.0 BNA MSY Nashville New Orleans TN LA
2060850.0 2014-02-06T08:50:00.000+0000 10.0 409.0 BNA MSY Nashville New Orleans TN LA
2061735.0 2014-02-06T17:35:00.000+0000 34.0 409.0 BNA MSY Nashville New Orleans TN LA
2071240.0 2014-02-07T12:40:00.000+0000 88.0 409.0 BNA MSY Nashville New Orleans TN LA
2071455.0 2014-02-07T14:55:00.000+0000 5.0 409.0 BNA MSY Nashville New Orleans TN LA
2070850.0 2014-02-07T08:50:00.000+0000 1.0 409.0 BNA MSY Nashville New Orleans TN LA
2071735.0 2014-02-07T17:35:00.000+0000 20.0 409.0 BNA MSY Nashville New Orleans TN LA
2081305.0 2014-02-08T13:05:00.000+0000 -6.0 409.0 BNA MSY Nashville New Orleans TN LA
2081805.0 2014-02-08T18:05:00.000+0000 0.0 409.0 BNA MSY Nashville New Orleans TN LA
2080950.0 2014-02-08T09:50:00.000+0000 -3.0 409.0 BNA MSY Nashville New Orleans TN LA
2091235.0 2014-02-09T12:35:00.000+0000 5.0 409.0 BNA MSY Nashville New Orleans TN LA
2091455.0 2014-02-09T14:55:00.000+0000 2.0 409.0 BNA MSY Nashville New Orleans TN LA
2091735.0 2014-02-09T17:35:00.000+0000 8.0 409.0 BNA MSY Nashville New Orleans TN LA
2101240.0 2014-02-10T12:40:00.000+0000 25.0 409.0 BNA MSY Nashville New Orleans TN LA
2101455.0 2014-02-10T14:55:00.000+0000 14.0 409.0 BNA MSY Nashville New Orleans TN LA
2100850.0 2014-02-10T08:50:00.000+0000 9.0 409.0 BNA MSY Nashville New Orleans TN LA
2101735.0 2014-02-10T17:35:00.000+0000 -2.0 409.0 BNA MSY Nashville New Orleans TN LA
2111240.0 2014-02-11T12:40:00.000+0000 145.0 409.0 BNA MSY Nashville New Orleans TN LA
2111455.0 2014-02-11T14:55:00.000+0000 -2.0 409.0 BNA MSY Nashville New Orleans TN LA
2110850.0 2014-02-11T08:50:00.000+0000 96.0 409.0 BNA MSY Nashville New Orleans TN LA
2111735.0 2014-02-11T17:35:00.000+0000 25.0 409.0 BNA MSY Nashville New Orleans TN LA
2121240.0 2014-02-12T12:40:00.000+0000 8.0 409.0 BNA MSY Nashville New Orleans TN LA
2121455.0 2014-02-12T14:55:00.000+0000 29.0 409.0 BNA MSY Nashville New Orleans TN LA
2120850.0 2014-02-12T08:50:00.000+0000 3.0 409.0 BNA MSY Nashville New Orleans TN LA
2121735.0 2014-02-12T17:35:00.000+0000 39.0 409.0 BNA MSY Nashville New Orleans TN LA
2131350.0 2014-02-13T13:50:00.000+0000 5.0 409.0 BNA MSY Nashville New Orleans TN LA
2131610.0 2014-02-13T16:10:00.000+0000 11.0 409.0 BNA MSY Nashville New Orleans TN LA
2130810.0 2014-02-13T08:10:00.000+0000 -4.0 409.0 BNA MSY Nashville New Orleans TN LA
2131800.0 2014-02-13T18:00:00.000+0000 9.0 409.0 BNA MSY Nashville New Orleans TN LA
2141610.0 2014-02-14T16:10:00.000+0000 37.0 409.0 BNA MSY Nashville New Orleans TN LA
2140810.0 2014-02-14T08:10:00.000+0000 13.0 409.0 BNA MSY Nashville New Orleans TN LA
2141350.0 2014-02-14T13:50:00.000+0000 46.0 409.0 BNA MSY Nashville New Orleans TN LA
2141800.0 2014-02-14T18:00:00.000+0000 21.0 409.0 BNA MSY Nashville New Orleans TN LA

Building the Graph

Now that we've imported our data, we're going to need to build our graph. To do so we're going to do two things. We are going to build the structure of the vertices (or nodes) and we're going to build the structure of the edges. What's awesome about GraphFrames is that this process is incredibly simple.

  • Rename IATA airport code to id in the Vertices Table
  • Start and End airports to src and dst for the Edges Table (flights)

These are required naming conventions for vertices and edges in GraphFrames.

WARNING: If the graphframes package, required in the cell below, is not installed, follow the instructions here.

// Note, ensure you have already installed the GraphFrames spack-package
import org.apache.spark.sql.functions._
import org.graphframes._

// Create Vertices (airports) and Edges (flights)
val tripVertices = airports.withColumnRenamed("IATA", "id").distinct()
val tripEdges = departureDelays_geo.select("tripid", "delay", "src", "dst", "city_dst", "state_dst")

// Cache Vertices and Edges
tripEdges.cache()
tripVertices.cache()
import org.apache.spark.sql.functions._
import org.graphframes._
tripVertices: org.apache.spark.sql.Dataset[org.apache.spark.sql.Row] = [id: string, City: string ... 2 more fields]
tripEdges: org.apache.spark.sql.DataFrame = [tripid: int, delay: int ... 4 more fields]
res5: tripVertices.type = [id: string, City: string ... 2 more fields]
// Vertices
// The vertices of our graph are the airports
display(tripVertices)
id City State Country
FAT Fresno CA USA
CMH Columbus OH USA
PHX Phoenix AZ USA
PAH Paducah KY USA
COS Colorado Springs CO USA
RNO Reno NV USA
MYR Myrtle Beach SC USA
VLD Valdosta GA USA
BPT Beaumont TX USA
CAE Columbia SC USA
PSC Pasco WA USA
SRQ Sarasota FL USA
LAX Los Angeles CA USA
DAY Dayton OH USA
AVP Wilkes-Barre PA USA
MFR Medford OR USA
JFK New York NY USA
BNA Nashville TN USA
CLT Charlotte NC USA
LAS Las Vegas NV USA
BDL Hartford CT USA
ILG Wilmington DE USA
ACT Waco TX USA
ATW Appleton WI USA
RHI Rhinelander WI USA
PWM Portland ME USA
SJT San Angelo TX USA
APN Alpena MI USA
GRB Green Bay WI USA
CAK Akron OH USA
LAN Lansing MI USA
FLL Fort Lauderdale FL USA
MSY New Orleans LA USA
SAT San Antonio TX USA
TPA Tampa FL USA
COD Cody WY USA
MOD Modesto CA USA
GTR Columbus MS USA
BTV Burlington VT USA
RDD Redding CA USA
HLN Helena MT USA
CPR Casper WY USA
FWA Fort Wayne IN USA
IMT Iron Mountain MI USA
DTW Detroit MI USA
BZN Bozeman MT USA
SBN South Bend IN USA
SPS Wichita Falls TX USA
BFL Bakersfield CA USA
HOB Hobbs NM USA
TVC Traverse City MI USA
CLE Cleveland OH USA
ABR Aberdeen SD USA
CHS Charleston SC USA
GUC Gunnison CO USA
IND Indianapolis IN USA
SDF Louisville KY USA
SAN San Diego CA USA
RSW Fort Myers FL USA
BOS Boston MA USA
TUL Tulsa OK USA
AGS Augusta GA USA
MOB Mobile AL USA
TUS Tucson AZ USA
KTN Ketchikan AK USA
BTR Baton Rouge LA USA
PNS Pensacola FL USA
ABQ Albuquerque NM USA
LGA New York NY USA
DAL Dallas TX USA
JNU Juneau AK USA
MAF Midland TX USA
RIC Richmond VA USA
FAR Fargo ND USA
MTJ Montrose CO USA
AMA Amarillo TX USA
ROC Rochester NY USA
SHV Shreveport LA USA
YAK Yakutat AK USA
CSG Columbus GA USA
ALO Waterloo IA USA
DRO Durango CO USA
CRP Corpus Christi TX USA
FNT Flint MI USA
GSO Greensboro NC USA
LWS Lewiston ID USA
TOL Toledo OH USA
GTF Great Falls MT USA
MKE Milwaukee WI USA
RKS Rock Springs WY USA
STL St. Louis MO USA
MHT Manchester NH USA
CRW Charleston WV USA
SLC Salt Lake City UT USA
ACV Eureka CA USA
DFW Dallas TX USA
OME Nome AK USA
ORF Norfolk VA USA
RDU Raleigh NC USA
SYR Syracuse NY USA
BQK Brunswick GA USA
ROA Roanoke VA USA
OKC Oklahoma City OK USA
EYW Key West FL USA
BOI Boise ID USA
ABY Albany GA USA
PIA Peoria IL USA
GRI Grand Island NE USA
PBI West Palm Beach FL USA
FSM Fort Smith AR USA
TYS Knoxville TN USA
DAB Daytona Beach FL USA
TTN Trenton NJ USA
MDT Harrisburg PA USA
AUS Austin TX USA
DCA Washington DC null USA
PIH Pocatello ID USA
GCC Gillette WY USA
BUR Burbank CA USA
GRK Killeen TX USA
LBB Lubbock TX USA
JAN Jackson MS USA
MSP Minneapolis MN USA
SAF Santa Fe NM USA
HPN White Plains NY USA
DHN Dothan AL USA
PSP Palm Springs CA USA
INL International Falls MN USA
CIC Chico CA USA
EGE Vail CO USA
CLD Carlsbad CA USA
RST Rochester MN USA
DEN Denver CO USA
EUG Eugene OR USA
LFT Lafayette LA USA
PVD Providence RI USA
DBQ Dubuque IA USA
SAV Savannah GA USA
SFO San Francisco CA USA
JAX Jacksonville FL USA
LIT Little Rock AR USA
IDA Idaho Falls ID USA
TYR Tyler TX USA
ANC Anchorage AK USA
HRL Harlingen TX USA
LMT Klamath Falls OR USA
PHF Newport News VA USA
HOU Houston TX USA
SPI Springfield IL USA
MOT Minot ND USA
BTM Butte MT USA
SMF Sacramento CA USA
HIB Hibbing MN USA
ROW Roswell NM USA
MBS Saginaw MI USA
ILM Wilmington NC USA
LGB Long Beach CA USA
IAD Washington DC null USA
ICT Wichita KS USA
BGR Bangor ME USA
ELP El Paso TX USA
SUX Sioux City IA USA
HSV Huntsville AL USA
SIT Sitka AK USA
CWA Wausau WI USA
LCH Lake Charles LA USA
CMI Champaign IL USA
ELM Elmira NY USA
CLL College Station TX USA
VPS Fort Walton Beach FL USA
MSN Madison WI USA
MHK Manhattan KS USA
OAJ Jacksonville NC USA
EKO Elko NV USA
FSD Sioux Falls SD USA
EWR Newark NJ USA
MEM Memphis TN USA
ADQ Kodiak AK USA
GGG Longview TX USA
BLI Bellingham WA USA
OMA Omaha NE USA
ATL Atlanta GA USA
SJC San Jose CA USA
SBA Santa Barbara CA USA
ONT Ontario CA USA
EAU Eau Claire WI USA
GPT Gulfport MS USA
SUN Sun Valley ID USA
CHO Charlottesville VA USA
MSO Missoula MT USA
CMX Hancock MI USA
ORD Chicago IL USA
EVV Evansville IN USA
MLU Monroe LA USA
LAW Lawton OK USA
BRW Barrow AK USA
SBP San Luis Obispo CA USA
LIH Lihue, Kauai HI USA
GJT Grand Junction CO USA
FAI Fairbanks AK USA
BIS Bismarck ND USA
SNA Orange County CA USA
LAR Laramie WY USA
JLN Joplin MO USA
LRD Laredo TX USA
LEX Lexington KY USA
SGU St. George UT USA
MCI Kansas City MO USA
AEX Alexandria LA USA
ISN Williston ND USA
TXK Texarkana AR USA
BIL Billings MT USA
CID Cedar Rapids IA USA
PDX Portland OR USA
ABE Allentown PA USA
DIK Dickinson ND USA
ART Watertown NY USA
GCK Garden City KS USA
BET Bethel AK USA
AVL Asheville NC USA
MCO Orlando FL USA
GSP Greenville SC USA
TWF Twin Falls ID USA
MKG Muskegon MI USA
FAY Fayetteville NC USA
SCE State College PA USA
EWN New Bern NC USA
XNA Fayetteville AR USA
MRY Monterey CA USA
MLB Melbourne FL USA
HNL Honolulu, Oahu HI USA
CVG Cincinnati OH USA
RAP Rapid City SD USA
AZO Kalamazoo MI USA
WRG Wrangell AK USA
ISP Islip NY USA
FLG Flagstaff AZ USA
BHM Birmingham AL USA
ALB Albany NY USA
SEA Seattle WA USA
GRR Grand Rapids MI USA
CHA Chattanooga TN USA
IAH Houston TX USA
SMX Santa Maria CA USA
MDW Chicago IL USA
MQT Marquette MI USA
LNK Lincoln NE USA
RDM Redmond OR USA
DLH Duluth MN USA
DSM Des Moines IA USA
OAK Oakland CA USA
PHL Philadelphia PA USA
FCA Kalispell MT USA
MFE McAllen TX USA
OGG Kahului, Maui HI USA
YUM Yuma AZ USA
BMI Bloomington IL USA
GEG Spokane WA USA
TLH Tallahassee FL USA
LSE La Crosse WI USA
MIA Miami FL USA
BRO Brownsville TX USA
JAC Jackson Hole WY USA
CDV Cordova AK USA
TRI Tri-City Airport TN USA
SWF Newburgh NY USA
MGM Montgomery AL USA
BWI Baltimore MD USA
SGF Springfield MO USA
GFK Grand Forks ND USA
GNV Gainesville FL USA
OTH North Bend OR USA
PIT Pittsburgh PA USA
BJI Bemidji MN USA
ASE Aspen CO USA
BUF Buffalo NY USA
COU Columbia MO USA
ABI Abilene TX USA
MLI Moline IL USA
// Edges
// The edges of our graph are the flights between airports
display(tripEdges)
tripid delay src dst city_dst state_dst
1011111.0 -5.0 MSP INL International Falls MN
1021111.0 7.0 MSP INL International Falls MN
1031111.0 0.0 MSP INL International Falls MN
1041925.0 0.0 MSP INL International Falls MN
1061115.0 33.0 MSP INL International Falls MN
1071115.0 23.0 MSP INL International Falls MN
1081115.0 -9.0 MSP INL International Falls MN
1091115.0 11.0 MSP INL International Falls MN
1101115.0 -3.0 MSP INL International Falls MN
1112015.0 -7.0 MSP INL International Falls MN
1121925.0 -5.0 MSP INL International Falls MN
1131115.0 -3.0 MSP INL International Falls MN
1141115.0 -6.0 MSP INL International Falls MN
1151115.0 -7.0 MSP INL International Falls MN
1161115.0 -3.0 MSP INL International Falls MN
1171115.0 4.0 MSP INL International Falls MN
1182015.0 -5.0 MSP INL International Falls MN
1191925.0 -7.0 MSP INL International Falls MN
1201115.0 -6.0 MSP INL International Falls MN
1211115.0 0.0 MSP INL International Falls MN
1221115.0 -4.0 MSP INL International Falls MN
1231115.0 -4.0 MSP INL International Falls MN
1241115.0 -3.0 MSP INL International Falls MN
1252015.0 -12.0 MSP INL International Falls MN
1261925.0 -5.0 MSP INL International Falls MN
1271115.0 0.0 MSP INL International Falls MN
1281115.0 -8.0 MSP INL International Falls MN
1291115.0 -2.0 MSP INL International Falls MN
1301115.0 0.0 MSP INL International Falls MN
1311115.0 -3.0 MSP INL International Falls MN
2012015.0 -4.0 MSP INL International Falls MN
2022015.0 0.0 MSP INL International Falls MN
2031115.0 -7.0 MSP INL International Falls MN
2041115.0 -6.0 MSP INL International Falls MN
2051115.0 -4.0 MSP INL International Falls MN
2061115.0 -2.0 MSP INL International Falls MN
2071115.0 -15.0 MSP INL International Falls MN
2082015.0 -4.0 MSP INL International Falls MN
2091925.0 1.0 MSP INL International Falls MN
2101115.0 -3.0 MSP INL International Falls MN
2111115.0 -7.0 MSP INL International Falls MN
2121115.0 -2.0 MSP INL International Falls MN
2131115.0 -3.0 MSP INL International Falls MN
2141115.0 -11.0 MSP INL International Falls MN
2152015.0 16.0 MSP INL International Falls MN
2161925.0 169.0 MSP INL International Falls MN
2171115.0 27.0 MSP INL International Falls MN
2181115.0 96.0 MSP INL International Falls MN
2191115.0 -9.0 MSP INL International Falls MN
2201115.0 -6.0 MSP INL International Falls MN
2211115.0 -4.0 MSP INL International Falls MN
2222015.0 -4.0 MSP INL International Falls MN
2231925.0 -3.0 MSP INL International Falls MN
2241115.0 -2.0 MSP INL International Falls MN
2251115.0 -6.0 MSP INL International Falls MN
2261115.0 -8.0 MSP INL International Falls MN
2271115.0 -8.0 MSP INL International Falls MN
2281115.0 5.0 MSP INL International Falls MN
3012015.0 -4.0 MSP INL International Falls MN
3022000.0 0.0 MSP INL International Falls MN
3031115.0 17.0 MSP INL International Falls MN
3041115.0 0.0 MSP INL International Falls MN
3051115.0 -7.0 MSP INL International Falls MN
3061115.0 -8.0 MSP INL International Falls MN
3071115.0 -10.0 MSP INL International Falls MN
3082000.0 -11.0 MSP INL International Falls MN
3092000.0 -9.0 MSP INL International Falls MN
3101115.0 -10.0 MSP INL International Falls MN
3111115.0 -8.0 MSP INL International Falls MN
3121115.0 -6.0 MSP INL International Falls MN
3131115.0 -8.0 MSP INL International Falls MN
3141115.0 -5.0 MSP INL International Falls MN
3152000.0 -11.0 MSP INL International Falls MN
3162000.0 -10.0 MSP INL International Falls MN
3171115.0 25.0 MSP INL International Falls MN
3181115.0 2.0 MSP INL International Falls MN
3191115.0 -5.0 MSP INL International Falls MN
3201115.0 -6.0 MSP INL International Falls MN
3211115.0 0.0 MSP INL International Falls MN
3222000.0 -10.0 MSP INL International Falls MN
3232000.0 -9.0 MSP INL International Falls MN
3241115.0 -9.0 MSP INL International Falls MN
3251115.0 -4.0 MSP INL International Falls MN
3261115.0 -5.0 MSP INL International Falls MN
3271115.0 9.0 MSP INL International Falls MN
3281115.0 -7.0 MSP INL International Falls MN
3292000.0 -19.0 MSP INL International Falls MN
3302000.0 -10.0 MSP INL International Falls MN
3311115.0 -8.0 MSP INL International Falls MN
2011230.0 -3.0 EWR MSY New Orleans LA
2010719.0 -2.0 EWR MSY New Orleans LA
2021230.0 -10.0 EWR MSY New Orleans LA
2020709.0 59.0 EWR MSY New Orleans LA
2021654.0 21.0 EWR MSY New Orleans LA
2030719.0 -6.0 EWR MSY New Orleans LA
2031659.0 0.0 EWR MSY New Orleans LA
2031230.0 0.0 EWR MSY New Orleans LA
2032043.0 0.0 EWR MSY New Orleans LA
2041230.0 24.0 EWR MSY New Orleans LA
2040719.0 168.0 EWR MSY New Orleans LA
2041730.0 88.0 EWR MSY New Orleans LA
2042043.0 106.0 EWR MSY New Orleans LA
2051659.0 0.0 EWR MSY New Orleans LA
2050719.0 0.0 EWR MSY New Orleans LA
2050929.0 0.0 EWR MSY New Orleans LA
2052043.0 46.0 EWR MSY New Orleans LA
2060719.0 -3.0 EWR MSY New Orleans LA
2061659.0 82.0 EWR MSY New Orleans LA
2061230.0 61.0 EWR MSY New Orleans LA
2062043.0 7.0 EWR MSY New Orleans LA
2070719.0 8.0 EWR MSY New Orleans LA
2071659.0 19.0 EWR MSY New Orleans LA
2071230.0 27.0 EWR MSY New Orleans LA
2072048.0 47.0 EWR MSY New Orleans LA
2081230.0 -10.0 EWR MSY New Orleans LA
2080719.0 -1.0 EWR MSY New Orleans LA
2091229.0 95.0 EWR MSY New Orleans LA
2091654.0 -5.0 EWR MSY New Orleans LA
2090709.0 -8.0 EWR MSY New Orleans LA
2092043.0 32.0 EWR MSY New Orleans LA
2100719.0 14.0 EWR MSY New Orleans LA
2101659.0 16.0 EWR MSY New Orleans LA
2101230.0 -4.0 EWR MSY New Orleans LA
2102043.0 -4.0 EWR MSY New Orleans LA
2111230.0 10.0 EWR MSY New Orleans LA
2110719.0 46.0 EWR MSY New Orleans LA
2111730.0 -9.0 EWR MSY New Orleans LA
2112043.0 -2.0 EWR MSY New Orleans LA
2120719.0 1.0 EWR MSY New Orleans LA
2121230.0 -4.0 EWR MSY New Orleans LA
2120929.0 89.0 EWR MSY New Orleans LA
2122043.0 36.0 EWR MSY New Orleans LA
2130738.0 0.0 EWR MSY New Orleans LA
2132041.0 0.0 EWR MSY New Orleans LA
2140729.0 0.0 EWR MSY New Orleans LA
2142041.0 0.0 EWR MSY New Orleans LA
2151206.0 0.0 EWR MSY New Orleans LA
2150659.0 0.0 EWR MSY New Orleans LA
2160705.0 -5.0 EWR MSY New Orleans LA
2170729.0 0.0 EWR MSY New Orleans LA
2172041.0 -7.0 EWR MSY New Orleans LA
2180738.0 0.0 EWR MSY New Orleans LA
2182041.0 36.0 EWR MSY New Orleans LA
2190727.0 15.0 EWR MSY New Orleans LA
2200738.0 -7.0 EWR MSY New Orleans LA
2202041.0 51.0 EWR MSY New Orleans LA
2210729.0 -2.0 EWR MSY New Orleans LA
2212041.0 0.0 EWR MSY New Orleans LA
2221206.0 -8.0 EWR MSY New Orleans LA
2220659.0 8.0 EWR MSY New Orleans LA
2232041.0 8.0 EWR MSY New Orleans LA
2230705.0 -10.0 EWR MSY New Orleans LA
2240729.0 6.0 EWR MSY New Orleans LA
2242041.0 -7.0 EWR MSY New Orleans LA
2250738.0 0.0 EWR MSY New Orleans LA
2260727.0 23.0 EWR MSY New Orleans LA
2262041.0 174.0 EWR MSY New Orleans LA
2270738.0 8.0 EWR MSY New Orleans LA
2272041.0 32.0 EWR MSY New Orleans LA
2280729.0 12.0 EWR MSY New Orleans LA
2282041.0 49.0 EWR MSY New Orleans LA
2281000.0 2.0 EWR MSY New Orleans LA
2051230.0 216.0 EWR MSY New Orleans LA
2131536.0 273.0 EWR MSY New Orleans LA
2141536.0 6.0 EWR MSY New Orleans LA
2151902.0 31.0 EWR MSY New Orleans LA
2151536.0 66.0 EWR MSY New Orleans LA
2162041.0 -4.0 EWR MSY New Orleans LA
2161536.0 7.0 EWR MSY New Orleans LA
2171536.0 3.0 EWR MSY New Orleans LA
2181536.0 26.0 EWR MSY New Orleans LA
2191536.0 -9.0 EWR MSY New Orleans LA
2201536.0 -3.0 EWR MSY New Orleans LA
2211536.0 34.0 EWR MSY New Orleans LA
2221900.0 -2.0 EWR MSY New Orleans LA
2221536.0 65.0 EWR MSY New Orleans LA
2231536.0 -3.0 EWR MSY New Orleans LA
2241536.0 -1.0 EWR MSY New Orleans LA
2251536.0 0.0 EWR MSY New Orleans LA
2261536.0 0.0 EWR MSY New Orleans LA
2271536.0 -4.0 EWR MSY New Orleans LA
2281536.0 8.0 EWR MSY New Orleans LA
2010730.0 -1.0 EWR MSY New Orleans LA
2021815.0 -1.0 EWR MSY New Orleans LA
2031815.0 0.0 EWR MSY New Orleans LA
2041815.0 -4.0 EWR MSY New Orleans LA
2051815.0 -4.0 EWR MSY New Orleans LA
2061815.0 -4.0 EWR MSY New Orleans LA
2071815.0 -5.0 EWR MSY New Orleans LA
2080730.0 -4.0 EWR MSY New Orleans LA
2091815.0 -1.0 EWR MSY New Orleans LA
2101815.0 -5.0 EWR MSY New Orleans LA
2111815.0 4.0 EWR MSY New Orleans LA
2121815.0 64.0 EWR MSY New Orleans LA
2131805.0 0.0 EWR MSY New Orleans LA
2141635.0 52.0 EWR MSY New Orleans LA
2150730.0 0.0 EWR MSY New Orleans LA
2161635.0 21.0 EWR MSY New Orleans LA
2171635.0 23.0 EWR MSY New Orleans LA
2181635.0 -5.0 EWR MSY New Orleans LA
2191635.0 21.0 EWR MSY New Orleans LA
2201635.0 0.0 EWR MSY New Orleans LA
2211635.0 292.0 EWR MSY New Orleans LA
2220730.0 28.0 EWR MSY New Orleans LA
2231635.0 0.0 EWR MSY New Orleans LA
2241635.0 -8.0 EWR MSY New Orleans LA
2251635.0 6.0 EWR MSY New Orleans LA
2261635.0 10.0 EWR MSY New Orleans LA
2271635.0 -1.0 EWR MSY New Orleans LA
2281635.0 -1.0 EWR MSY New Orleans LA
3011206.0 -5.0 EWR MSY New Orleans LA
3010659.0 -1.0 EWR MSY New Orleans LA
3022041.0 0.0 EWR MSY New Orleans LA
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3200950.0 3.0 MCI MSY New Orleans LA
3210950.0 7.0 MCI MSY New Orleans LA
3221610.0 38.0 MCI MSY New Orleans LA
3230950.0 -1.0 MCI MSY New Orleans LA
3240950.0 0.0 MCI MSY New Orleans LA
3250950.0 4.0 MCI MSY New Orleans LA
3260950.0 5.0 MCI MSY New Orleans LA
3270950.0 12.0 MCI MSY New Orleans LA
3280950.0 0.0 MCI MSY New Orleans LA
3291610.0 12.0 MCI MSY New Orleans LA
3300950.0 -2.0 MCI MSY New Orleans LA
3310950.0 3.0 MCI MSY New Orleans LA
1011635.0 -7.0 MCI MSY New Orleans LA
1021635.0 96.0 MCI MSY New Orleans LA
1031635.0 3.0 MCI MSY New Orleans LA
1041205.0 1.0 MCI MSY New Orleans LA
1051635.0 60.0 MCI MSY New Orleans LA
1061635.0 -7.0 MCI MSY New Orleans LA
1071105.0 14.0 MCI MSY New Orleans LA
1081105.0 4.0 MCI MSY New Orleans LA
1091105.0 11.0 MCI MSY New Orleans LA
1101105.0 -1.0 MCI MSY New Orleans LA
1111530.0 11.0 MCI MSY New Orleans LA
1121105.0 0.0 MCI MSY New Orleans LA
1131105.0 -5.0 MCI MSY New Orleans LA
1141105.0 1.0 MCI MSY New Orleans LA
1151105.0 9.0 MCI MSY New Orleans LA
1161105.0 1.0 MCI MSY New Orleans LA
1171105.0 -1.0 MCI MSY New Orleans LA
1181530.0 48.0 MCI MSY New Orleans LA
1191105.0 0.0 MCI MSY New Orleans LA
1201105.0 -4.0 MCI MSY New Orleans LA
1211105.0 2.0 MCI MSY New Orleans LA
1221105.0 19.0 MCI MSY New Orleans LA
1231105.0 -2.0 MCI MSY New Orleans LA
1241105.0 72.0 MCI MSY New Orleans LA
1251530.0 5.0 MCI MSY New Orleans LA
1261105.0 -5.0 MCI MSY New Orleans LA
1271105.0 -6.0 MCI MSY New Orleans LA
1281105.0 0.0 MCI MSY New Orleans LA
1291105.0 0.0 MCI MSY New Orleans LA
1301105.0 1.0 MCI MSY New Orleans LA
1311105.0 1.0 MCI MSY New Orleans LA
3011530.0 72.0 BNA MSY New Orleans LA
3010850.0 2.0 BNA MSY New Orleans LA
3011245.0 4.0 BNA MSY New Orleans LA
3021610.0 14.0 BNA MSY New Orleans LA
3021350.0 15.0 BNA MSY New Orleans LA
3021800.0 56.0 BNA MSY New Orleans LA
3031610.0 13.0 BNA MSY New Orleans LA
3030810.0 0.0 BNA MSY New Orleans LA
3031350.0 -1.0 BNA MSY New Orleans LA
3031800.0 -5.0 BNA MSY New Orleans LA
3041610.0 -3.0 BNA MSY New Orleans LA
3040810.0 -4.0 BNA MSY New Orleans LA
3041350.0 10.0 BNA MSY New Orleans LA
3041800.0 7.0 BNA MSY New Orleans LA
3051610.0 -1.0 BNA MSY New Orleans LA
3050810.0 11.0 BNA MSY New Orleans LA
3051350.0 48.0 BNA MSY New Orleans LA
3051800.0 21.0 BNA MSY New Orleans LA
3061610.0 26.0 BNA MSY New Orleans LA
3060810.0 -5.0 BNA MSY New Orleans LA
3061350.0 13.0 BNA MSY New Orleans LA
3061800.0 5.0 BNA MSY New Orleans LA
3071610.0 12.0 BNA MSY New Orleans LA
3070810.0 -3.0 BNA MSY New Orleans LA
3071350.0 10.0 BNA MSY New Orleans LA
3071800.0 7.0 BNA MSY New Orleans LA
3081540.0 27.0 BNA MSY New Orleans LA
3081335.0 -4.0 BNA MSY New Orleans LA
3080945.0 11.0 BNA MSY New Orleans LA
3091620.0 0.0 BNA MSY New Orleans LA
3091820.0 25.0 BNA MSY New Orleans LA
3091420.0 12.0 BNA MSY New Orleans LA
3100820.0 -1.0 BNA MSY New Orleans LA
3101420.0 41.0 BNA MSY New Orleans LA
3101820.0 11.0 BNA MSY New Orleans LA
3101620.0 7.0 BNA MSY New Orleans LA
3110820.0 3.0 BNA MSY New Orleans LA
3111420.0 15.0 BNA MSY New Orleans LA
3111820.0 29.0 BNA MSY New Orleans LA
3111620.0 5.0 BNA MSY New Orleans LA
3120820.0 12.0 BNA MSY New Orleans LA
3121420.0 40.0 BNA MSY New Orleans LA
3121820.0 15.0 BNA MSY New Orleans LA
3121620.0 24.0 BNA MSY New Orleans LA
3130820.0 126.0 BNA MSY New Orleans LA
3131420.0 13.0 BNA MSY New Orleans LA
3131820.0 55.0 BNA MSY New Orleans LA
3131620.0 40.0 BNA MSY New Orleans LA
3140820.0 -2.0 BNA MSY New Orleans LA
3141420.0 35.0 BNA MSY New Orleans LA
3141820.0 21.0 BNA MSY New Orleans LA
3141620.0 36.0 BNA MSY New Orleans LA
3151335.0 -3.0 BNA MSY New Orleans LA
3150945.0 3.0 BNA MSY New Orleans LA
3151540.0 -3.0 BNA MSY New Orleans LA
3161620.0 22.0 BNA MSY New Orleans LA
3161820.0 39.0 BNA MSY New Orleans LA
3161420.0 0.0 BNA MSY New Orleans LA
3170820.0 1.0 BNA MSY New Orleans LA
3171420.0 112.0 BNA MSY New Orleans LA
3171820.0 12.0 BNA MSY New Orleans LA
3171620.0 56.0 BNA MSY New Orleans LA
3180820.0 0.0 BNA MSY New Orleans LA
3181420.0 25.0 BNA MSY New Orleans LA
3181820.0 36.0 BNA MSY New Orleans LA
3181620.0 1.0 BNA MSY New Orleans LA
3190820.0 -2.0 BNA MSY New Orleans LA
3191420.0 54.0 BNA MSY New Orleans LA
3191820.0 7.0 BNA MSY New Orleans LA
3191620.0 29.0 BNA MSY New Orleans LA
3200820.0 0.0 BNA MSY New Orleans LA
3201420.0 18.0 BNA MSY New Orleans LA
3201820.0 9.0 BNA MSY New Orleans LA
3201620.0 79.0 BNA MSY New Orleans LA
3210820.0 3.0 BNA MSY New Orleans LA
3211420.0 22.0 BNA MSY New Orleans LA
3211820.0 30.0 BNA MSY New Orleans LA
3211620.0 22.0 BNA MSY New Orleans LA
3221335.0 -2.0 BNA MSY New Orleans LA
3220945.0 0.0 BNA MSY New Orleans LA
3221540.0 -1.0 BNA MSY New Orleans LA
3231620.0 -2.0 BNA MSY New Orleans LA
3231820.0 6.0 BNA MSY New Orleans LA
3231420.0 -3.0 BNA MSY New Orleans LA
3240820.0 0.0 BNA MSY New Orleans LA
3241420.0 27.0 BNA MSY New Orleans LA
3241820.0 44.0 BNA MSY New Orleans LA
3241620.0 41.0 BNA MSY New Orleans LA
3250820.0 0.0 BNA MSY New Orleans LA
3251420.0 70.0 BNA MSY New Orleans LA
3251820.0 30.0 BNA MSY New Orleans LA
3251620.0 30.0 BNA MSY New Orleans LA
3260820.0 -1.0 BNA MSY New Orleans LA
3261420.0 8.0 BNA MSY New Orleans LA
3261820.0 1.0 BNA MSY New Orleans LA
3261620.0 -4.0 BNA MSY New Orleans LA
3270820.0 0.0 BNA MSY New Orleans LA
3271420.0 25.0 BNA MSY New Orleans LA
3271820.0 41.0 BNA MSY New Orleans LA
3271620.0 23.0 BNA MSY New Orleans LA
3280820.0 -5.0 BNA MSY New Orleans LA
3281420.0 52.0 BNA MSY New Orleans LA
3281820.0 17.0 BNA MSY New Orleans LA
3281620.0 15.0 BNA MSY New Orleans LA
3291335.0 1.0 BNA MSY New Orleans LA
3290945.0 20.0 BNA MSY New Orleans LA
3291540.0 35.0 BNA MSY New Orleans LA
3301620.0 0.0 BNA MSY New Orleans LA
3301820.0 22.0 BNA MSY New Orleans LA
3301420.0 10.0 BNA MSY New Orleans LA
3310820.0 -1.0 BNA MSY New Orleans LA
3311420.0 19.0 BNA MSY New Orleans LA
3311820.0 25.0 BNA MSY New Orleans LA
3311620.0 30.0 BNA MSY New Orleans LA
1010800.0 -3.0 BNA MSY New Orleans LA
1011210.0 7.0 BNA MSY New Orleans LA
1011835.0 53.0 BNA MSY New Orleans LA
1021215.0 43.0 BNA MSY New Orleans LA
1021835.0 200.0 BNA MSY New Orleans LA
1020800.0 29.0 BNA MSY New Orleans LA
1031215.0 185.0 BNA MSY New Orleans LA
1031835.0 226.0 BNA MSY New Orleans LA
1030800.0 -1.0 BNA MSY New Orleans LA
1041420.0 174.0 BNA MSY New Orleans LA
1040835.0 18.0 BNA MSY New Orleans LA
1051215.0 85.0 BNA MSY New Orleans LA
1051835.0 283.0 BNA MSY New Orleans LA
1050800.0 3.0 BNA MSY New Orleans LA
1061215.0 150.0 BNA MSY New Orleans LA
1061835.0 133.0 BNA MSY New Orleans LA
1060800.0 102.0 BNA MSY New Orleans LA
1071240.0 57.0 BNA MSY New Orleans LA
1071455.0 12.0 BNA MSY New Orleans LA
1070905.0 5.0 BNA MSY New Orleans LA
1071735.0 131.0 BNA MSY New Orleans LA
1081240.0 19.0 BNA MSY New Orleans LA
1081455.0 2.0 BNA MSY New Orleans LA
1080905.0 -2.0 BNA MSY New Orleans LA
1081735.0 34.0 BNA MSY New Orleans LA
1091240.0 14.0 BNA MSY New Orleans LA
1091455.0 24.0 BNA MSY New Orleans LA
1090905.0 -1.0 BNA MSY New Orleans LA
1091735.0 28.0 BNA MSY New Orleans LA
1101240.0 50.0 BNA MSY New Orleans LA
1101455.0 11.0 BNA MSY New Orleans LA
1100905.0 4.0 BNA MSY New Orleans LA
1101735.0 33.0 BNA MSY New Orleans LA
1111305.0 0.0 BNA MSY New Orleans LA
1111805.0 2.0 BNA MSY New Orleans LA
1110950.0 0.0 BNA MSY New Orleans LA
1121235.0 8.0 BNA MSY New Orleans LA
1121455.0 4.0 BNA MSY New Orleans LA
1121735.0 4.0 BNA MSY New Orleans LA
1131240.0 9.0 BNA MSY New Orleans LA
1131455.0 2.0 BNA MSY New Orleans LA
1130850.0 -1.0 BNA MSY New Orleans LA
1131735.0 15.0 BNA MSY New Orleans LA
1141240.0 17.0 BNA MSY New Orleans LA
1141455.0 -1.0 BNA MSY New Orleans LA
1140850.0 -4.0 BNA MSY New Orleans LA
1141735.0 7.0 BNA MSY New Orleans LA
1151240.0 -2.0 BNA MSY New Orleans LA
1151455.0 1.0 BNA MSY New Orleans LA
1150850.0 -2.0 BNA MSY New Orleans LA
1151735.0 9.0 BNA MSY New Orleans LA
1161240.0 17.0 BNA MSY New Orleans LA
1161455.0 17.0 BNA MSY New Orleans LA
1160850.0 -2.0 BNA MSY New Orleans LA
1161735.0 52.0 BNA MSY New Orleans LA
1171240.0 21.0 BNA MSY New Orleans LA
1171455.0 13.0 BNA MSY New Orleans LA
1170850.0 10.0 BNA MSY New Orleans LA
1171735.0 40.0 BNA MSY New Orleans LA
1181305.0 2.0 BNA MSY New Orleans LA
1181805.0 42.0 BNA MSY New Orleans LA
1180950.0 4.0 BNA MSY New Orleans LA
1191235.0 23.0 BNA MSY New Orleans LA
1191455.0 4.0 BNA MSY New Orleans LA
1191735.0 64.0 BNA MSY New Orleans LA
1201240.0 8.0 BNA MSY New Orleans LA
1201455.0 5.0 BNA MSY New Orleans LA
1200850.0 7.0 BNA MSY New Orleans LA
1201735.0 -3.0 BNA MSY New Orleans LA
1211240.0 41.0 BNA MSY New Orleans LA
1211455.0 -1.0 BNA MSY New Orleans LA
1210850.0 18.0 BNA MSY New Orleans LA
1211735.0 17.0 BNA MSY New Orleans LA
1221240.0 19.0 BNA MSY New Orleans LA
1221455.0 -1.0 BNA MSY New Orleans LA
1220850.0 -4.0 BNA MSY New Orleans LA
1221735.0 118.0 BNA MSY New Orleans LA
1231240.0 20.0 BNA MSY New Orleans LA
1231455.0 4.0 BNA MSY New Orleans LA
1230850.0 18.0 BNA MSY New Orleans LA
1231735.0 33.0 BNA MSY New Orleans LA
1241240.0 20.0 BNA MSY New Orleans LA
1241455.0 4.0 BNA MSY New Orleans LA
1240850.0 12.0 BNA MSY New Orleans LA
1241735.0 0.0 BNA MSY New Orleans LA
1251305.0 27.0 BNA MSY New Orleans LA
1251805.0 19.0 BNA MSY New Orleans LA
1250950.0 -2.0 BNA MSY New Orleans LA
1261235.0 0.0 BNA MSY New Orleans LA
1261455.0 5.0 BNA MSY New Orleans LA
1261735.0 3.0 BNA MSY New Orleans LA
1271240.0 17.0 BNA MSY New Orleans LA
1271455.0 -3.0 BNA MSY New Orleans LA
1270850.0 -2.0 BNA MSY New Orleans LA
1271735.0 10.0 BNA MSY New Orleans LA
1281240.0 0.0 BNA MSY New Orleans LA
1281455.0 0.0 BNA MSY New Orleans LA
1280850.0 0.0 BNA MSY New Orleans LA
1281735.0 0.0 BNA MSY New Orleans LA
1291240.0 13.0 BNA MSY New Orleans LA
1291455.0 -2.0 BNA MSY New Orleans LA
1290850.0 0.0 BNA MSY New Orleans LA
1291735.0 9.0 BNA MSY New Orleans LA
1301240.0 38.0 BNA MSY New Orleans LA
1301455.0 6.0 BNA MSY New Orleans LA
1300850.0 -1.0 BNA MSY New Orleans LA
1301735.0 57.0 BNA MSY New Orleans LA
1311240.0 31.0 BNA MSY New Orleans LA
1311455.0 22.0 BNA MSY New Orleans LA
1310850.0 -2.0 BNA MSY New Orleans LA
1311735.0 6.0 BNA MSY New Orleans LA
2011305.0 -1.0 BNA MSY New Orleans LA
2011805.0 -6.0 BNA MSY New Orleans LA
2010950.0 4.0 BNA MSY New Orleans LA
2021455.0 11.0 BNA MSY New Orleans LA
2021235.0 26.0 BNA MSY New Orleans LA
2021650.0 77.0 BNA MSY New Orleans LA
2031240.0 30.0 BNA MSY New Orleans LA
2031455.0 10.0 BNA MSY New Orleans LA
2030850.0 -1.0 BNA MSY New Orleans LA
2031735.0 -3.0 BNA MSY New Orleans LA
2041240.0 56.0 BNA MSY New Orleans LA
2041455.0 23.0 BNA MSY New Orleans LA
2040850.0 -1.0 BNA MSY New Orleans LA
2041735.0 3.0 BNA MSY New Orleans LA
2051240.0 33.0 BNA MSY New Orleans LA
2051455.0 14.0 BNA MSY New Orleans LA
2050850.0 19.0 BNA MSY New Orleans LA
2051735.0 26.0 BNA MSY New Orleans LA
2061240.0 43.0 BNA MSY New Orleans LA
2061455.0 -2.0 BNA MSY New Orleans LA
2060850.0 10.0 BNA MSY New Orleans LA
2061735.0 34.0 BNA MSY New Orleans LA
2071240.0 88.0 BNA MSY New Orleans LA
2071455.0 5.0 BNA MSY New Orleans LA
2070850.0 1.0 BNA MSY New Orleans LA
2071735.0 20.0 BNA MSY New Orleans LA
2081305.0 -6.0 BNA MSY New Orleans LA
2081805.0 0.0 BNA MSY New Orleans LA
2080950.0 -3.0 BNA MSY New Orleans LA
2091235.0 5.0 BNA MSY New Orleans LA
2091455.0 2.0 BNA MSY New Orleans LA
2091735.0 8.0 BNA MSY New Orleans LA
2101240.0 25.0 BNA MSY New Orleans LA
2101455.0 14.0 BNA MSY New Orleans LA
2100850.0 9.0 BNA MSY New Orleans LA
2101735.0 -2.0 BNA MSY New Orleans LA
2111240.0 145.0 BNA MSY New Orleans LA
2111455.0 -2.0 BNA MSY New Orleans LA
2110850.0 96.0 BNA MSY New Orleans LA
2111735.0 25.0 BNA MSY New Orleans LA
2121240.0 8.0 BNA MSY New Orleans LA
2121455.0 29.0 BNA MSY New Orleans LA
2120850.0 3.0 BNA MSY New Orleans LA
2121735.0 39.0 BNA MSY New Orleans LA
2131350.0 5.0 BNA MSY New Orleans LA
2131610.0 11.0 BNA MSY New Orleans LA
2130810.0 -4.0 BNA MSY New Orleans LA
2131800.0 9.0 BNA MSY New Orleans LA
2141610.0 37.0 BNA MSY New Orleans LA
2140810.0 13.0 BNA MSY New Orleans LA
2141350.0 46.0 BNA MSY New Orleans LA
2141800.0 21.0 BNA MSY New Orleans LA
// Build `tripGraph` GraphFrame
// This GraphFrame builds up on the vertices and edges based on our trips (flights)
val tripGraph = GraphFrame(tripVertices, tripEdges)
println(tripGraph)

// Build `tripGraphPrime` GraphFrame
// This graphframe contains a smaller subset of data to make it easier to display motifs and subgraphs (below)
val tripEdgesPrime = departureDelays_geo.select("tripid", "delay", "src", "dst")
val tripGraphPrime = GraphFrame(tripVertices, tripEdgesPrime)
GraphFrame(v:[id: string, City: string ... 2 more fields], e:[src: string, dst: string ... 4 more fields])
tripGraph: org.graphframes.GraphFrame = GraphFrame(v:[id: string, City: string ... 2 more fields], e:[src: string, dst: string ... 4 more fields])
tripEdgesPrime: org.apache.spark.sql.DataFrame = [tripid: int, delay: int ... 2 more fields]
tripGraphPrime: org.graphframes.GraphFrame = GraphFrame(v:[id: string, City: string ... 2 more fields], e:[src: string, dst: string ... 2 more fields])

Simple Queries

Let's start with a set of simple graph queries to understand flight performance and departure delays

println(s"Airports: ${tripGraph.vertices.count()}")
println(s"Trips: ${tripGraph.edges.count()}")
Airports: 279
Trips: 1361141
// Finding the longest Delay
val longestDelay = tripGraph.edges.groupBy().max("delay")
display(longestDelay)
max(delay)
1642.0
1642.0/60.0
res13: Double = 27.366666666666667
// Determining number of on-time / early flights vs. delayed flights
println(s"On-time / Early Flights: ${tripGraph.edges.filter("delay <= 0").count()}")
println(s"Delayed Flights: ${tripGraph.edges.filter("delay > 0").count()}")
On-time / Early Flights: 780469
Delayed Flights: 580672

What flights departing SFO are most likely to have significant delays

Note, delay can be <= 0 meaning the flight left on time or early

//tripGraph.createOrReplaceTempView("tripgraph")
val sfoDelayedTrips = tripGraph.edges.
  filter("src = 'SFO' and delay > 0").
  groupBy("src", "dst").
  avg("delay").
  sort(desc("avg(delay)"))
sfoDelayedTrips: org.apache.spark.sql.Dataset[org.apache.spark.sql.Row] = [src: string, dst: string ... 1 more field]
display(sfoDelayedTrips)
src dst avg(delay)
SFO OKC 59.073170731707314
SFO JAC 57.13333333333333
SFO COS 53.976190476190474
SFO OTH 48.09090909090909
SFO SAT 47.625
SFO MOD 46.80952380952381
SFO SUN 46.723404255319146
SFO CIC 46.72164948453608
SFO ABQ 44.8125
SFO ASE 44.285714285714285
SFO PIT 43.875
SFO MIA 43.81730769230769
SFO FAT 43.23972602739726
SFO MFR 43.11848341232228
SFO SBP 43.09770114942529
SFO MSP 42.766917293233085
SFO BOI 42.65482233502538
SFO RDM 41.98823529411764
SFO AUS 41.690677966101696
SFO SLC 41.407272727272726
SFO JFK 41.01379310344828
SFO PSP 40.909909909909906
SFO PHX 40.67272727272727
SFO MRY 40.61764705882353
SFO ACV 40.3728813559322
SFO LAS 40.107602339181284
SFO TUS 39.853658536585364
SFO SAN 38.97361809045226
SFO SBA 38.758620689655174
SFO BFL 38.51136363636363
SFO RDU 38.170731707317074
SFO STL 38.13513513513514
SFO IND 38.114285714285714
SFO EUG 37.573913043478264
SFO RNO 36.81372549019608
SFO BUR 36.75675675675676
SFO LGB 36.752941176470586
SFO HNL 36.25367647058823
SFO LAX 36.165543071161046
SFO RDD 36.11009174311926
SFO MSY 35.421052631578945
SFO SMF 34.936
SFO MDW 34.824742268041234
SFO FLL 34.76842105263158
SFO SEA 34.68854961832061
SFO MCI 34.68571428571428
SFO DFW 34.36642599277978
SFO OGG 34.171875
SFO PDX 34.14430894308943
SFO ORD 33.991130820399114
SFO LIH 32.93023255813954
SFO DEN 32.861491628614914
SFO PSC 32.604651162790695
SFO PHL 32.440677966101696
SFO BWI 31.70212765957447
SFO ONT 31.49079754601227
SFO SNA 31.18426103646833
SFO MCO 31.03488372093023
SFO MKE 31.03448275862069
SFO CLE 30.979591836734695
SFO EWR 30.354285714285716
SFO BOS 29.623471882640587
SFO LMT 29.233333333333334
SFO DTW 28.34722222222222
SFO IAH 28.322105263157894
SFO CVG 27.03125
SFO ATL 26.84860557768924
SFO IAD 26.125964010282775
SFO ANC 25.5
SFO BZN 23.964285714285715
SFO CLT 22.636363636363637
SFO DCA 21.896103896103895
// After displaying tripDelays, use Plot Options to set `state_dst` as a Key.
val tripDelays = tripGraph.edges.filter($"delay" > 0)
display(tripDelays)
tripid delay src dst city_dst state_dst
1021111.0 7.0 MSP INL International Falls MN
1061115.0 33.0 MSP INL International Falls MN
1071115.0 23.0 MSP INL International Falls MN
1091115.0 11.0 MSP INL International Falls MN
1171115.0 4.0 MSP INL International Falls MN
2091925.0 1.0 MSP INL International Falls MN
2152015.0 16.0 MSP INL International Falls MN
2161925.0 169.0 MSP INL International Falls MN
2171115.0 27.0 MSP INL International Falls MN
2181115.0 96.0 MSP INL International Falls MN
2281115.0 5.0 MSP INL International Falls MN
3031115.0 17.0 MSP INL International Falls MN
3171115.0 25.0 MSP INL International Falls MN
3181115.0 2.0 MSP INL International Falls MN
3271115.0 9.0 MSP INL International Falls MN
2020709.0 59.0 EWR MSY New Orleans LA
2021654.0 21.0 EWR MSY New Orleans LA
2041230.0 24.0 EWR MSY New Orleans LA
2040719.0 168.0 EWR MSY New Orleans LA
2041730.0 88.0 EWR MSY New Orleans LA
2042043.0 106.0 EWR MSY New Orleans LA
2052043.0 46.0 EWR MSY New Orleans LA
2061659.0 82.0 EWR MSY New Orleans LA
2061230.0 61.0 EWR MSY New Orleans LA
2062043.0 7.0 EWR MSY New Orleans LA
2070719.0 8.0 EWR MSY New Orleans LA
2071659.0 19.0 EWR MSY New Orleans LA
2071230.0 27.0 EWR MSY New Orleans LA
2072048.0 47.0 EWR MSY New Orleans LA
2091229.0 95.0 EWR MSY New Orleans LA
2092043.0 32.0 EWR MSY New Orleans LA
2100719.0 14.0 EWR MSY New Orleans LA
2101659.0 16.0 EWR MSY New Orleans LA
2111230.0 10.0 EWR MSY New Orleans LA
2110719.0 46.0 EWR MSY New Orleans LA
2120719.0 1.0 EWR MSY New Orleans LA
2120929.0 89.0 EWR MSY New Orleans LA
2122043.0 36.0 EWR MSY New Orleans LA
2182041.0 36.0 EWR MSY New Orleans LA
2190727.0 15.0 EWR MSY New Orleans LA
2202041.0 51.0 EWR MSY New Orleans LA
2220659.0 8.0 EWR MSY New Orleans LA
2232041.0 8.0 EWR MSY New Orleans LA
2240729.0 6.0 EWR MSY New Orleans LA
2260727.0 23.0 EWR MSY New Orleans LA
2262041.0 174.0 EWR MSY New Orleans LA
2270738.0 8.0 EWR MSY New Orleans LA
2272041.0 32.0 EWR MSY New Orleans LA
2280729.0 12.0 EWR MSY New Orleans LA
2282041.0 49.0 EWR MSY New Orleans LA
2281000.0 2.0 EWR MSY New Orleans LA
2051230.0 216.0 EWR MSY New Orleans LA
2131536.0 273.0 EWR MSY New Orleans LA
2141536.0 6.0 EWR MSY New Orleans LA
2151902.0 31.0 EWR MSY New Orleans LA
2151536.0 66.0 EWR MSY New Orleans LA
2161536.0 7.0 EWR MSY New Orleans LA
2171536.0 3.0 EWR MSY New Orleans LA
2181536.0 26.0 EWR MSY New Orleans LA
2211536.0 34.0 EWR MSY New Orleans LA
2221536.0 65.0 EWR MSY New Orleans LA
2281536.0 8.0 EWR MSY New Orleans LA
2111815.0 4.0 EWR MSY New Orleans LA
2121815.0 64.0 EWR MSY New Orleans LA
2141635.0 52.0 EWR MSY New Orleans LA
2161635.0 21.0 EWR MSY New Orleans LA
2171635.0 23.0 EWR MSY New Orleans LA
2191635.0 21.0 EWR MSY New Orleans LA
2211635.0 292.0 EWR MSY New Orleans LA
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2251635.0 6.0 EWR MSY New Orleans LA
2261635.0 10.0 EWR MSY New Orleans LA
3032041.0 113.0 EWR MSY New Orleans LA
3052041.0 4.0 EWR MSY New Orleans LA
3061252.0 67.0 EWR MSY New Orleans LA
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3081250.0 5.0 EWR MSY New Orleans LA
3112059.0 181.0 EWR MSY New Orleans LA
3122059.0 22.0 EWR MSY New Orleans LA
3121252.0 161.0 EWR MSY New Orleans LA
3140705.0 66.0 EWR MSY New Orleans LA
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3151250.0 34.0 EWR MSY New Orleans LA
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3172059.0 132.0 EWR MSY New Orleans LA
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3192059.0 16.0 EWR MSY New Orleans LA
3202059.0 77.0 EWR MSY New Orleans LA
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3252059.0 121.0 EWR MSY New Orleans LA
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3302059.0 166.0 EWR MSY New Orleans LA
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3131825.0 123.0 EWR MSY New Orleans LA
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3191825.0 223.0 EWR MSY New Orleans LA
3201825.0 178.0 EWR MSY New Orleans LA
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3301825.0 139.0 EWR MSY New Orleans LA
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1071730.0 161.0 EWR MSY New Orleans LA
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1051815.0 172.0 EWR MSY New Orleans LA
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1241815.0 84.0 EWR MSY New Orleans LA
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3291940.0 231.0 LAS MSY New Orleans LA
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1031805.0 154.0 LAS MSY New Orleans LA
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1051805.0 53.0 LAS MSY New Orleans LA
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1071750.0 302.0 LAS MSY New Orleans LA
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1301750.0 35.0 LAS MSY New Orleans LA
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2041105.0 1.0 MCI MSY New Orleans LA
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2200830.0 9.0 MCI MSY New Orleans LA
2230930.0 2.0 MCI MSY New Orleans LA
2240830.0 3.0 MCI MSY New Orleans LA
2260830.0 251.0 MCI MSY New Orleans LA
3020930.0 35.0 MCI MSY New Orleans LA
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3040830.0 11.0 MCI MSY New Orleans LA
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3081610.0 93.0 MCI MSY New Orleans LA
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3110950.0 36.0 MCI MSY New Orleans LA
3120950.0 68.0 MCI MSY New Orleans LA
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3151610.0 16.0 MCI MSY New Orleans LA
3180950.0 1.0 MCI MSY New Orleans LA
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3291610.0 12.0 MCI MSY New Orleans LA
3310950.0 3.0 MCI MSY New Orleans LA
1021635.0 96.0 MCI MSY New Orleans LA
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1051635.0 60.0 MCI MSY New Orleans LA
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1241105.0 72.0 MCI MSY New Orleans LA
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1301105.0 1.0 MCI MSY New Orleans LA
1311105.0 1.0 MCI MSY New Orleans LA
3011530.0 72.0 BNA MSY New Orleans LA
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3021610.0 14.0 BNA MSY New Orleans LA
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3050810.0 11.0 BNA MSY New Orleans LA
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3111420.0 15.0 BNA MSY New Orleans LA
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3130820.0 126.0 BNA MSY New Orleans LA
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1021835.0 200.0 BNA MSY New Orleans LA
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2071735.0 20.0 BNA MSY New Orleans LA
2091235.0 5.0 BNA MSY New Orleans LA
2091455.0 2.0 BNA MSY New Orleans LA
2091735.0 8.0 BNA MSY New Orleans LA
2101240.0 25.0 BNA MSY New Orleans LA
2101455.0 14.0 BNA MSY New Orleans LA
2100850.0 9.0 BNA MSY New Orleans LA
2111240.0 145.0 BNA MSY New Orleans LA
2110850.0 96.0 BNA MSY New Orleans LA
2111735.0 25.0 BNA MSY New Orleans LA
2121240.0 8.0 BNA MSY New Orleans LA
2121455.0 29.0 BNA MSY New Orleans LA
2120850.0 3.0 BNA MSY New Orleans LA
2121735.0 39.0 BNA MSY New Orleans LA
2131350.0 5.0 BNA MSY New Orleans LA
2131610.0 11.0 BNA MSY New Orleans LA
2131800.0 9.0 BNA MSY New Orleans LA
2141610.0 37.0 BNA MSY New Orleans LA
2140810.0 13.0 BNA MSY New Orleans LA
2141350.0 46.0 BNA MSY New Orleans LA
2141800.0 21.0 BNA MSY New Orleans LA
2151530.0 35.0 BNA MSY New Orleans LA
2150850.0 7.0 BNA MSY New Orleans LA
2161800.0 17.0 BNA MSY New Orleans LA
2170810.0 1.0 BNA MSY New Orleans LA
2171350.0 1.0 BNA MSY New Orleans LA
2180810.0 11.0 BNA MSY New Orleans LA
2181350.0 40.0 BNA MSY New Orleans LA
2181800.0 1.0 BNA MSY New Orleans LA
2191350.0 7.0 BNA MSY New Orleans LA
2191800.0 21.0 BNA MSY New Orleans LA
2201610.0 1.0 BNA MSY New Orleans LA
2200810.0 16.0 BNA MSY New Orleans LA
2201350.0 5.0 BNA MSY New Orleans LA
2201800.0 162.0 BNA MSY New Orleans LA
2211610.0 46.0 BNA MSY New Orleans LA
2210810.0 1.0 BNA MSY New Orleans LA
2211350.0 10.0 BNA MSY New Orleans LA
2211800.0 10.0 BNA MSY New Orleans LA
2221530.0 1.0 BNA MSY New Orleans LA
2231350.0 2.0 BNA MSY New Orleans LA
2231800.0 6.0 BNA MSY New Orleans LA
2241350.0 12.0 BNA MSY New Orleans LA
2250810.0 26.0 BNA MSY New Orleans LA
2251800.0 103.0 BNA MSY New Orleans LA
2261610.0 7.0 BNA MSY New Orleans LA
2260810.0 1.0 BNA MSY New Orleans LA
2261350.0 11.0 BNA MSY New Orleans LA
2261800.0 6.0 BNA MSY New Orleans LA
2271800.0 9.0 BNA MSY New Orleans LA
2281610.0 23.0 BNA MSY New Orleans LA
2281350.0 8.0 BNA MSY New Orleans LA
2281800.0 4.0 BNA MSY New Orleans LA
3011117.0 36.0 CLT MSY New Orleans LA
3011635.0 77.0 CLT MSY New Orleans LA
3021117.0 30.0 CLT MSY New Orleans LA
3031825.0 9.0 CLT MSY New Orleans LA
3061825.0 32.0 CLT MSY New Orleans LA
3062010.0 33.0 CLT MSY New Orleans LA
3070750.0 3.0 CLT MSY New Orleans LA
3071435.0 16.0 CLT MSY New Orleans LA
3081115.0 28.0 CLT MSY New Orleans LA
3091115.0 28.0 CLT MSY New Orleans LA
3090909.0 118.0 CLT MSY New Orleans LA
3102010.0 4.0 CLT MSY New Orleans LA
3110750.0 27.0 CLT MSY New Orleans LA
3121115.0 16.0 CLT MSY New Orleans LA
3122010.0 31.0 CLT MSY New Orleans LA
3121435.0 5.0 CLT MSY New Orleans LA
3141825.0 28.0 CLT MSY New Orleans LA
3141115.0 5.0 CLT MSY New Orleans LA
3140915.0 17.0 CLT MSY New Orleans LA
3161840.0 24.0 CLT MSY New Orleans LA
3162010.0 34.0 CLT MSY New Orleans LA
3161435.0 2.0 CLT MSY New Orleans LA
3171825.0 23.0 CLT MSY New Orleans LA
3171115.0 2.0 CLT MSY New Orleans LA
3172010.0 2.0 CLT MSY New Orleans LA
3171435.0 8.0 CLT MSY New Orleans LA
3170915.0 8.0 CLT MSY New Orleans LA
3180750.0 46.0 CLT MSY New Orleans LA
3182010.0 1.0 CLT MSY New Orleans LA
3180915.0 5.0 CLT MSY New Orleans LA
3190915.0 65.0 CLT MSY New Orleans LA
3202010.0 24.0 CLT MSY New Orleans LA
3201435.0 5.0 CLT MSY New Orleans LA
3210750.0 2.0 CLT MSY New Orleans LA
3230909.0 14.0 CLT MSY New Orleans LA
3241115.0 21.0 CLT MSY New Orleans LA
3240915.0 4.0 CLT MSY New Orleans LA
3251435.0 56.0 CLT MSY New Orleans LA
3250915.0 1.0 CLT MSY New Orleans LA
3261115.0 9.0 CLT MSY New Orleans LA
3261435.0 96.0 CLT MSY New Orleans LA
3260915.0 8.0 CLT MSY New Orleans LA
3271115.0 1.0 CLT MSY New Orleans LA
3270915.0 23.0 CLT MSY New Orleans LA
3281115.0 37.0 CLT MSY New Orleans LA
3282010.0 46.0 CLT MSY New Orleans LA
3291825.0 150.0 CLT MSY New Orleans LA
3291115.0 3.0 CLT MSY New Orleans LA
3292010.0 53.0 CLT MSY New Orleans LA
3291635.0 8.0 CLT MSY New Orleans LA
3290915.0 2.0 CLT MSY New Orleans LA
3311115.0 18.0 CLT MSY New Orleans LA
3311435.0 1.0 CLT MSY New Orleans LA
1011815.0 11.0 CLT MSY New Orleans LA
1011435.0 40.0 CLT MSY New Orleans LA
1021815.0 22.0 CLT MSY New Orleans LA
1022015.0 2.0 CLT MSY New Orleans LA
1021435.0 1.0 CLT MSY New Orleans LA
1042020.0 53.0 CLT MSY New Orleans LA
1041435.0 15.0 CLT MSY New Orleans LA
1051815.0 45.0 CLT MSY New Orleans LA
1052015.0 19.0 CLT MSY New Orleans LA
1051435.0 60.0 CLT MSY New Orleans LA
1060750.0 7.0 CLT MSY New Orleans LA
1061120.0 15.0 CLT MSY New Orleans LA
1071825.0 58.0 CLT MSY New Orleans LA
1071435.0 11.0 CLT MSY New Orleans LA
1081435.0 13.0 CLT MSY New Orleans LA
1080915.0 1.0 CLT MSY New Orleans LA
1091117.0 13.0 CLT MSY New Orleans LA
1100750.0 21.0 CLT MSY New Orleans LA
1101825.0 8.0 CLT MSY New Orleans LA
1101117.0 27.0 CLT MSY New Orleans LA
1101635.0 55.0 CLT MSY New Orleans LA
1101435.0 13.0 CLT MSY New Orleans LA
1110750.0 115.0 CLT MSY New Orleans LA
1111117.0 49.0 CLT MSY New Orleans LA
1111635.0 145.0 CLT MSY New Orleans LA
1112010.0 2.0 CLT MSY New Orleans LA
1111435.0 126.0 CLT MSY New Orleans LA
1110915.0 72.0 CLT MSY New Orleans LA
1121117.0 5.0 CLT MSY New Orleans LA
1121435.0 1.0 CLT MSY New Orleans LA
1131435.0 3.0 CLT MSY New Orleans LA
1151117.0 16.0 CLT MSY New Orleans LA
1151435.0 2.0 CLT MSY New Orleans LA
1171117.0 16.0 CLT MSY New Orleans LA
1181117.0 3.0 CLT MSY New Orleans LA
1180915.0 14.0 CLT MSY New Orleans LA
1191117.0 2.0 CLT MSY New Orleans LA
1200750.0 51.0 CLT MSY New Orleans LA
1211825.0 2.0 CLT MSY New Orleans LA
1211435.0 4.0 CLT MSY New Orleans LA
1221117.0 10.0 CLT MSY New Orleans LA
1221435.0 25.0 CLT MSY New Orleans LA
1230750.0 23.0 CLT MSY New Orleans LA
1231117.0 27.0 CLT MSY New Orleans LA
1231635.0 4.0 CLT MSY New Orleans LA
1230915.0 131.0 CLT MSY New Orleans LA
1241117.0 5.0 CLT MSY New Orleans LA
1252010.0 1.0 CLT MSY New Orleans LA
1250915.0 2.0 CLT MSY New Orleans LA
1271825.0 27.0 CLT MSY New Orleans LA
1271117.0 52.0 CLT MSY New Orleans LA
1290750.0 26.0 CLT MSY New Orleans LA
1291117.0 19.0 CLT MSY New Orleans LA
1291635.0 21.0 CLT MSY New Orleans LA
1291435.0 6.0 CLT MSY New Orleans LA
1290915.0 1.0 CLT MSY New Orleans LA
1311825.0 50.0 CLT MSY New Orleans LA
1310915.0 1.0 CLT MSY New Orleans LA
2011117.0 30.0 CLT MSY New Orleans LA
2011635.0 23.0 CLT MSY New Orleans LA
2010900.0 2.0 CLT MSY New Orleans LA
2031117.0 8.0 CLT MSY New Orleans LA
2031435.0 6.0 CLT MSY New Orleans LA
2041117.0 22.0 CLT MSY New Orleans LA
2051117.0 36.0 CLT MSY New Orleans LA
2051435.0 13.0 CLT MSY New Orleans LA
2050915.0 7.0 CLT MSY New Orleans LA
2060750.0 34.0 CLT MSY New Orleans LA
2061117.0 3.0 CLT MSY New Orleans LA
2061635.0 14.0 CLT MSY New Orleans LA
2071825.0 11.0 CLT MSY New Orleans LA
2090915.0 79.0 CLT MSY New Orleans LA
2101435.0 4.0 CLT MSY New Orleans LA
2121635.0 42.0 CLT MSY New Orleans LA
2121435.0 1.0 CLT MSY New Orleans LA
2140750.0 151.0 CLT MSY New Orleans LA
2141825.0 33.0 CLT MSY New Orleans LA
2142010.0 28.0 CLT MSY New Orleans LA
2141435.0 13.0 CLT MSY New Orleans LA
2140915.0 174.0 CLT MSY New Orleans LA
2150915.0 4.0 CLT MSY New Orleans LA
2161117.0 27.0 CLT MSY New Orleans LA
2161435.0 12.0 CLT MSY New Orleans LA
2171117.0 2.0 CLT MSY New Orleans LA
2171435.0 2.0 CLT MSY New Orleans LA
2170915.0 30.0 CLT MSY New Orleans LA
2200915.0 6.0 CLT MSY New Orleans LA
2211117.0 2.0 CLT MSY New Orleans LA
2211435.0 24.0 CLT MSY New Orleans LA
2210915.0 52.0 CLT MSY New Orleans LA
2232010.0 74.0 CLT MSY New Orleans LA
2251435.0 5.0 CLT MSY New Orleans LA
2261825.0 53.0 CLT MSY New Orleans LA
2272010.0 10.0 CLT MSY New Orleans LA
2271435.0 16.0 CLT MSY New Orleans LA
2280750.0 2.0 CLT MSY New Orleans LA
2281117.0 3.0 CLT MSY New Orleans LA
3011715.0 20.0 DAL MSY New Orleans LA
3011830.0 124.0 DAL MSY New Orleans LA
3021710.0 174.0 DAL MSY New Orleans LA
3021335.0 30.0 DAL MSY New Orleans LA
3022025.0 84.0 DAL MSY New Orleans LA
3021855.0 55.0 DAL MSY New Orleans LA
3030605.0 19.0 DAL MSY New Orleans LA
3031335.0 22.0 DAL MSY New Orleans LA
3032025.0 2.0 DAL MSY New Orleans LA
3030920.0 2.0 DAL MSY New Orleans LA
3031710.0 29.0 DAL MSY New Orleans LA
3031100.0 3.0 DAL MSY New Orleans LA
3031855.0 3.0 DAL MSY New Orleans LA
3041335.0 15.0 DAL MSY New Orleans LA
3042025.0 13.0 DAL MSY New Orleans LA
3052025.0 16.0 DAL MSY New Orleans LA
3051710.0 45.0 DAL MSY New Orleans LA
3051855.0 17.0 DAL MSY New Orleans LA
3061335.0 24.0 DAL MSY New Orleans LA
3062025.0 52.0 DAL MSY New Orleans LA
3060920.0 30.0 DAL MSY New Orleans LA
3061710.0 16.0 DAL MSY New Orleans LA
3061100.0 22.0 DAL MSY New Orleans LA
3070805.0 9.0 DAL MSY New Orleans LA
3071335.0 60.0 DAL MSY New Orleans LA
3072025.0 26.0 DAL MSY New Orleans LA
3071710.0 12.0 DAL MSY New Orleans LA
3071100.0 13.0 DAL MSY New Orleans LA
3071855.0 66.0 DAL MSY New Orleans LA
3081440.0 107.0 DAL MSY New Orleans LA
3081745.0 4.0 DAL MSY New Orleans LA
3091900.0 15.0 DAL MSY New Orleans LA
3092055.0 35.0 DAL MSY New Orleans LA
3091810.0 15.0 DAL MSY New Orleans LA
3091455.0 2.0 DAL MSY New Orleans LA
3101900.0 15.0 DAL MSY New Orleans LA
3102055.0 21.0 DAL MSY New Orleans LA
3101810.0 7.0 DAL MSY New Orleans LA
3111900.0 19.0 DAL MSY New Orleans LA
3112055.0 103.0 DAL MSY New Orleans LA
3111205.0 15.0 DAL MSY New Orleans LA
3110825.0 3.0 DAL MSY New Orleans LA
3111810.0 7.0 DAL MSY New Orleans LA
3111455.0 4.0 DAL MSY New Orleans LA
3121900.0 50.0 DAL MSY New Orleans LA
3122055.0 57.0 DAL MSY New Orleans LA
3121205.0 30.0 DAL MSY New Orleans LA
3120825.0 2.0 DAL MSY New Orleans LA
3121810.0 9.0 DAL MSY New Orleans LA
3131900.0 70.0 DAL MSY New Orleans LA
3130930.0 7.0 DAL MSY New Orleans LA
3132055.0 77.0 DAL MSY New Orleans LA
3130600.0 3.0 DAL MSY New Orleans LA
3130825.0 4.0 DAL MSY New Orleans LA
3131810.0 10.0 DAL MSY New Orleans LA
3141900.0 28.0 DAL MSY New Orleans LA
3142055.0 25.0 DAL MSY New Orleans LA
3140600.0 8.0 DAL MSY New Orleans LA
3141205.0 54.0 DAL MSY New Orleans LA
3141810.0 1.0 DAL MSY New Orleans LA
3141455.0 4.0 DAL MSY New Orleans LA
3150830.0 2.0 DAL MSY New Orleans LA
3151440.0 5.0 DAL MSY New Orleans LA
3161900.0 15.0 DAL MSY New Orleans LA
3162055.0 22.0 DAL MSY New Orleans LA
3161810.0 5.0 DAL MSY New Orleans LA
3160930.0 7.0 DAL MSY New Orleans LA
3171900.0 83.0 DAL MSY New Orleans LA
3170930.0 1.0 DAL MSY New Orleans LA
3172055.0 81.0 DAL MSY New Orleans LA
3170825.0 7.0 DAL MSY New Orleans LA
3171810.0 20.0 DAL MSY New Orleans LA
3181900.0 46.0 DAL MSY New Orleans LA
3182055.0 148.0 DAL MSY New Orleans LA
3180600.0 8.0 DAL MSY New Orleans LA
3181205.0 32.0 DAL MSY New Orleans LA
3180825.0 7.0 DAL MSY New Orleans LA
3181810.0 92.0 DAL MSY New Orleans LA
3181455.0 11.0 DAL MSY New Orleans LA
3191900.0 29.0 DAL MSY New Orleans LA
3192055.0 71.0 DAL MSY New Orleans LA
3191205.0 10.0 DAL MSY New Orleans LA
3191810.0 11.0 DAL MSY New Orleans LA
3191455.0 2.0 DAL MSY New Orleans LA
3201900.0 26.0 DAL MSY New Orleans LA
3202055.0 34.0 DAL MSY New Orleans LA
3200600.0 19.0 DAL MSY New Orleans LA
3201205.0 4.0 DAL MSY New Orleans LA
3200825.0 5.0 DAL MSY New Orleans LA
3201810.0 31.0 DAL MSY New Orleans LA
3211900.0 52.0 DAL MSY New Orleans LA
3212055.0 23.0 DAL MSY New Orleans LA
3210600.0 1.0 DAL MSY New Orleans LA
3211205.0 29.0 DAL MSY New Orleans LA
3210825.0 13.0 DAL MSY New Orleans LA
3211810.0 14.0 DAL MSY New Orleans LA
3211455.0 9.0 DAL MSY New Orleans LA
3221750.0 7.0 DAL MSY New Orleans LA
3221440.0 23.0 DAL MSY New Orleans LA
3231900.0 36.0 DAL MSY New Orleans LA
3231810.0 6.0 DAL MSY New Orleans LA
3231455.0 8.0 DAL MSY New Orleans LA
3231210.0 16.0 DAL MSY New Orleans LA
3231045.0 13.0 DAL MSY New Orleans LA
3230930.0 6.0 DAL MSY New Orleans LA
3241900.0 15.0 DAL MSY New Orleans LA
3242055.0 36.0 DAL MSY New Orleans LA
3241205.0 23.0 DAL MSY New Orleans LA
3240825.0 5.0 DAL MSY New Orleans LA
3241810.0 9.0 DAL MSY New Orleans LA
3241455.0 17.0 DAL MSY New Orleans LA
3251900.0 58.0 DAL MSY New Orleans LA
3252055.0 51.0 DAL MSY New Orleans LA
3251205.0 5.0 DAL MSY New Orleans LA
3250825.0 5.0 DAL MSY New Orleans LA
3251810.0 17.0 DAL MSY New Orleans LA
3251455.0 10.0 DAL MSY New Orleans LA
3261900.0 15.0 DAL MSY New Orleans LA
3262055.0 69.0 DAL MSY New Orleans LA
3261205.0 6.0 DAL MSY New Orleans LA
3260825.0 3.0 DAL MSY New Orleans LA
3261810.0 20.0 DAL MSY New Orleans LA
3261455.0 10.0 DAL MSY New Orleans LA
3271900.0 36.0 DAL MSY New Orleans LA
3272055.0 78.0 DAL MSY New Orleans LA
3271205.0 17.0 DAL MSY New Orleans LA
3270825.0 8.0 DAL MSY New Orleans LA
3271810.0 45.0 DAL MSY New Orleans LA
3271455.0 11.0 DAL MSY New Orleans LA
3281900.0 46.0 DAL MSY New Orleans LA
3280930.0 11.0 DAL MSY New Orleans LA
3282055.0 65.0 DAL MSY New Orleans LA
3281205.0 13.0 DAL MSY New Orleans LA
3280825.0 6.0 DAL MSY New Orleans LA
3281810.0 49.0 DAL MSY New Orleans LA
3281455.0 1.0 DAL MSY New Orleans LA
3290830.0 1.0 DAL MSY New Orleans LA
3291440.0 7.0 DAL MSY New Orleans LA
3301900.0 126.0 DAL MSY New Orleans LA
3301810.0 4.0 DAL MSY New Orleans LA
3301455.0 4.0 DAL MSY New Orleans LA
3301045.0 29.0 DAL MSY New Orleans LA
3300930.0 4.0 DAL MSY New Orleans LA
3311900.0 47.0 DAL MSY New Orleans LA
3310930.0 10.0 DAL MSY New Orleans LA
3312055.0 3.0 DAL MSY New Orleans LA
3311205.0 20.0 DAL MSY New Orleans LA
3310825.0 21.0 DAL MSY New Orleans LA
3311810.0 18.0 DAL MSY New Orleans LA
3311455.0 3.0 DAL MSY New Orleans LA
1012115.0 24.0 DAL MSY New Orleans LA
1011235.0 8.0 DAL MSY New Orleans LA
1011650.0 70.0 DAL MSY New Orleans LA
1011525.0 21.0 DAL MSY New Orleans LA
1011120.0 5.0 DAL MSY New Orleans LA
1021120.0 40.0 DAL MSY New Orleans LA
1021650.0 37.0 DAL MSY New Orleans LA
1020925.0 3.0 DAL MSY New Orleans LA
1022110.0 115.0 DAL MSY New Orleans LA
1021235.0 66.0 DAL MSY New Orleans LA
1020605.0 31.0 DAL MSY New Orleans LA
1021525.0 91.0 DAL MSY New Orleans LA
1021910.0 12.0 DAL MSY New Orleans LA
1031120.0 121.0 DAL MSY New Orleans LA
1031650.0 154.0 DAL MSY New Orleans LA
1030925.0 46.0 DAL MSY New Orleans LA
1032110.0 120.0 DAL MSY New Orleans LA
1031235.0 43.0 DAL MSY New Orleans LA
1031525.0 45.0 DAL MSY New Orleans LA
1031910.0 194.0 DAL MSY New Orleans LA
1040710.0 6.0 DAL MSY New Orleans LA
1041730.0 108.0 DAL MSY New Orleans LA
1041420.0 49.0 DAL MSY New Orleans LA
1040930.0 45.0 DAL MSY New Orleans LA
1041540.0 1.0 DAL MSY New Orleans LA
1052110.0 110.0 DAL MSY New Orleans LA
1051235.0 3.0 DAL MSY New Orleans LA
1051525.0 24.0 DAL MSY New Orleans LA
1051150.0 32.0 DAL MSY New Orleans LA
1051910.0 29.0 DAL MSY New Orleans LA
1050925.0 11.0 DAL MSY New Orleans LA
1051650.0 101.0 DAL MSY New Orleans LA
1061120.0 48.0 DAL MSY New Orleans LA
1061650.0 29.0 DAL MSY New Orleans LA
1062110.0 103.0 DAL MSY New Orleans LA
1061235.0 71.0 DAL MSY New Orleans LA
1061525.0 18.0 DAL MSY New Orleans LA
1072015.0 46.0 DAL MSY New Orleans LA
1071535.0 53.0 DAL MSY New Orleans LA
1070630.0 1.0 DAL MSY New Orleans LA
1071930.0 1.0 DAL MSY New Orleans LA
1070925.0 17.0 DAL MSY New Orleans LA
1071025.0 22.0 DAL MSY New Orleans LA
1071230.0 2.0 DAL MSY New Orleans LA
1071635.0 2.0 DAL MSY New Orleans LA
1082015.0 28.0 DAL MSY New Orleans LA
1081535.0 31.0 DAL MSY New Orleans LA
1081930.0 16.0 DAL MSY New Orleans LA
1080925.0 4.0 DAL MSY New Orleans LA
1081025.0 24.0 DAL MSY New Orleans LA
1081230.0 8.0 DAL MSY New Orleans LA
1081635.0 29.0 DAL MSY New Orleans LA
1092015.0 89.0 DAL MSY New Orleans LA
1091535.0 20.0 DAL MSY New Orleans LA
1090925.0 39.0 DAL MSY New Orleans LA
1091025.0 94.0 DAL MSY New Orleans LA
1091230.0 73.0 DAL MSY New Orleans LA
1091635.0 35.0 DAL MSY New Orleans LA
1102015.0 100.0 DAL MSY New Orleans LA
1101535.0 70.0 DAL MSY New Orleans LA
1101930.0 118.0 DAL MSY New Orleans LA
1100925.0 10.0 DAL MSY New Orleans LA
1101025.0 9.0 DAL MSY New Orleans LA
1101230.0 21.0 DAL MSY New Orleans LA
1101635.0 57.0 DAL MSY New Orleans LA
1111750.0 36.0 DAL MSY New Orleans LA
1110645.0 2.0 DAL MSY New Orleans LA
1111450.0 3.0 DAL MSY New Orleans LA
1111625.0 50.0 DAL MSY New Orleans LA
1122015.0 2.0 DAL MSY New Orleans LA
1121535.0 8.0 DAL MSY New Orleans LA
1121620.0 33.0 DAL MSY New Orleans LA
1121930.0 23.0 DAL MSY New Orleans LA
1120925.0 3.0 DAL MSY New Orleans LA
1121230.0 6.0 DAL MSY New Orleans LA
1131535.0 3.0 DAL MSY New Orleans LA
1130630.0 2.0 DAL MSY New Orleans LA
1130925.0 9.0 DAL MSY New Orleans LA
1131025.0 18.0 DAL MSY New Orleans LA
1142015.0 10.0 DAL MSY New Orleans LA
1140630.0 5.0 DAL MSY New Orleans LA
1140925.0 12.0 DAL MSY New Orleans LA
1141025.0 16.0 DAL MSY New Orleans LA
1141230.0 3.0 DAL MSY New Orleans LA
1141635.0 5.0 DAL MSY New Orleans LA
1151930.0 1.0 DAL MSY New Orleans LA
1150925.0 8.0 DAL MSY New Orleans LA
1151025.0 19.0 DAL MSY New Orleans LA
1162015.0 6.0 DAL MSY New Orleans LA
1161535.0 26.0 DAL MSY New Orleans LA
1161930.0 5.0 DAL MSY New Orleans LA
1160925.0 10.0 DAL MSY New Orleans LA
1161025.0 23.0 DAL MSY New Orleans LA
1161230.0 4.0 DAL MSY New Orleans LA
1161635.0 28.0 DAL MSY New Orleans LA
1172015.0 17.0 DAL MSY New Orleans LA
1171535.0 2.0 DAL MSY New Orleans LA
1171025.0 3.0 DAL MSY New Orleans LA
1171230.0 17.0 DAL MSY New Orleans LA
1171635.0 30.0 DAL MSY New Orleans LA
1180645.0 19.0 DAL MSY New Orleans LA
1181450.0 3.0 DAL MSY New Orleans LA
1181625.0 7.0 DAL MSY New Orleans LA
1191535.0 23.0 DAL MSY New Orleans LA
1191620.0 4.0 DAL MSY New Orleans LA
1191930.0 219.0 DAL MSY New Orleans LA
1190925.0 5.0 DAL MSY New Orleans LA
1200925.0 12.0 DAL MSY New Orleans LA
1201025.0 33.0 DAL MSY New Orleans LA
1201230.0 1.0 DAL MSY New Orleans LA
1201635.0 6.0 DAL MSY New Orleans LA
1211535.0 95.0 DAL MSY New Orleans LA
// States with the longest cumulative delays (with individual delays > 100 minutes) (origin: Seattle)
display(tripGraph.edges.filter($"src" === "SEA" && $"delay" > 100))
tripid delay src dst city_dst state_dst
3201938.0 108.0 SEA BUR Burbank CA
3201655.0 107.0 SEA SNA Orange County CA
1011950.0 123.0 SEA OAK Oakland CA
1021950.0 194.0 SEA OAK Oakland CA
1021615.0 317.0 SEA OAK Oakland CA
1021755.0 385.0 SEA OAK Oakland CA
1031950.0 283.0 SEA OAK Oakland CA
1031615.0 364.0 SEA OAK Oakland CA
1031325.0 130.0 SEA OAK Oakland CA
1061755.0 107.0 SEA OAK Oakland CA
1081330.0 118.0 SEA OAK Oakland CA
2282055.0 150.0 SEA OAK Oakland CA
3061600.0 130.0 SEA OAK Oakland CA
3170815.0 199.0 SEA DCA Washington DC null
2151845.0 128.0 SEA KTN Ketchikan AK
2281845.0 104.0 SEA KTN Ketchikan AK
3130720.0 117.0 SEA KTN Ketchikan AK
1011411.0 177.0 SEA IAH Houston TX
1022347.0 158.0 SEA IAH Houston TX
1021411.0 170.0 SEA IAH Houston TX
1031201.0 116.0 SEA IAH Houston TX
1031900.0 178.0 SEA IAH Houston TX
1042347.0 114.0 SEA IAH Houston TX
1062347.0 136.0 SEA IAH Houston TX
1101203.0 173.0 SEA IAH Houston TX
1172300.0 125.0 SEA IAH Houston TX
1250605.0 227.0 SEA IAH Houston TX
1291203.0 106.0 SEA IAH Houston TX
2141157.0 127.0 SEA IAH Houston TX
2150740.0 466.0 SEA IAH Houston TX
2180750.0 105.0 SEA IAH Houston TX
3010740.0 103.0 SEA IAH Houston TX
3021152.0 124.0 SEA IAH Houston TX
3121152.0 340.0 SEA IAH Houston TX
3140600.0 139.0 SEA IAH Houston TX
3171152.0 121.0 SEA IAH Houston TX
3280600.0 103.0 SEA IAH Houston TX
1151746.0 229.0 SEA HNL Honolulu, Oahu HI
1271746.0 111.0 SEA HNL Honolulu, Oahu HI
1030840.0 294.0 SEA HNL Honolulu, Oahu HI
2091035.0 132.0 SEA HNL Honolulu, Oahu HI
3141035.0 295.0 SEA HNL Honolulu, Oahu HI
3141930.0 128.0 SEA HNL Honolulu, Oahu HI
3311930.0 104.0 SEA HNL Honolulu, Oahu HI
3030840.0 185.0 SEA HNL Honolulu, Oahu HI
3240845.0 114.0 SEA HNL Honolulu, Oahu HI
1041740.0 256.0 SEA SJC San Jose CA
1061815.0 200.0 SEA SJC San Jose CA
3031600.0 161.0 SEA SJC San Jose CA
1031100.0 145.0 SEA LGB Long Beach CA
1041737.0 320.0 SEA LGB Long Beach CA
1081728.0 122.0 SEA LGB Long Beach CA
1221140.0 189.0 SEA LGB Long Beach CA
2121140.0 365.0 SEA LGB Long Beach CA
3070710.0 115.0 SEA LGB Long Beach CA
3180935.0 135.0 SEA LGB Long Beach CA
2141245.0 176.0 SEA RNO Reno NV
1052147.0 110.0 SEA BOS Boston MA
1081420.0 109.0 SEA BOS Boston MA
1112313.0 110.0 SEA BOS Boston MA
1232313.0 110.0 SEA BOS Boston MA
2140945.0 105.0 SEA BOS Boston MA
2032313.0 114.0 SEA BOS Boston MA
2121420.0 108.0 SEA BOS Boston MA
2141415.0 152.0 SEA BOS Boston MA
3282307.0 119.0 SEA BOS Boston MA
1110905.0 130.0 SEA EWR Newark NJ
1022227.0 236.0 SEA EWR Newark NJ
1180703.0 138.0 SEA EWR Newark NJ
2030905.0 212.0 SEA EWR Newark NJ
3141530.0 131.0 SEA EWR Newark NJ
3171530.0 181.0 SEA EWR Newark NJ
3202200.0 168.0 SEA EWR Newark NJ
1032115.0 196.0 SEA LAS Las Vegas NV
1201840.0 113.0 SEA LAS Las Vegas NV
1260840.0 165.0 SEA LAS Las Vegas NV
1261840.0 121.0 SEA LAS Las Vegas NV
1031905.0 103.0 SEA LAS Las Vegas NV
1041550.0 156.0 SEA LAS Las Vegas NV
1061820.0 213.0 SEA LAS Las Vegas NV
1061515.0 116.0 SEA LAS Las Vegas NV
1080805.0 235.0 SEA LAS Las Vegas NV
1170800.0 247.0 SEA LAS Las Vegas NV
2191235.0 210.0 SEA LAS Las Vegas NV
2281430.0 121.0 SEA LAS Las Vegas NV
2281235.0 187.0 SEA LAS Las Vegas NV
2170830.0 610.0 SEA LAS Las Vegas NV
2051205.0 110.0 SEA LAS Las Vegas NV
2111835.0 133.0 SEA LAS Las Vegas NV
2132005.0 135.0 SEA LAS Las Vegas NV
2272005.0 102.0 SEA LAS Las Vegas NV
3031430.0 108.0 SEA LAS Las Vegas NV
3141410.0 102.0 SEA LAS Las Vegas NV
3151205.0 103.0 SEA LAS Las Vegas NV
3281245.0 140.0 SEA LAS Las Vegas NV
3181520.0 103.0 SEA LAS Las Vegas NV
3292000.0 107.0 SEA LAS Las Vegas NV
1051955.0 160.0 SEA FAI Fairbanks AK
1040955.0 126.0 SEA DEN Denver CO
1040650.0 103.0 SEA DEN Denver CO
1160650.0 120.0 SEA DEN Denver CO
1011940.0 167.0 SEA DEN Denver CO
1041039.0 113.0 SEA DEN Denver CO
1041437.0 256.0 SEA DEN Denver CO
1041937.0 191.0 SEA DEN Denver CO
1040605.0 138.0 SEA DEN Denver CO
1061937.0 111.0 SEA DEN Denver CO
1121937.0 118.0 SEA DEN Denver CO
1171937.0 104.0 SEA DEN Denver CO
1021523.0 118.0 SEA DEN Denver CO
1041521.0 177.0 SEA DEN Denver CO
1061055.0 154.0 SEA DEN Denver CO
1281515.0 137.0 SEA DEN Denver CO
1011450.0 102.0 SEA DEN Denver CO
1021205.0 425.0 SEA DEN Denver CO
1031450.0 211.0 SEA DEN Denver CO
2210955.0 132.0 SEA DEN Denver CO
2111537.0 156.0 SEA DEN Denver CO
2110700.0 625.0 SEA DEN Denver CO
2191039.0 148.0 SEA DEN Denver CO
2211039.0 105.0 SEA DEN Denver CO
2031055.0 174.0 SEA DEN Denver CO
2051055.0 112.0 SEA DEN Denver CO
2211110.0 106.0 SEA DEN Denver CO
3131405.0 154.0 SEA DEN Denver CO
3181930.0 115.0 SEA DEN Denver CO
3191749.0 103.0 SEA DEN Denver CO
3011405.0 109.0 SEA DEN Denver CO
3121519.0 231.0 SEA DEN Denver CO
3061445.0 148.0 SEA DEN Denver CO
3181440.0 132.0 SEA DEN Denver CO
1011306.0 206.0 SEA IAD Washington DC null
1050806.0 105.0 SEA IAD Washington DC null
1052226.0 111.0 SEA IAD Washington DC null
1291256.0 108.0 SEA IAD Washington DC null
2031256.0 185.0 SEA IAD Washington DC null
2041256.0 129.0 SEA IAD Washington DC null
2101256.0 144.0 SEA IAD Washington DC null
2191316.0 122.0 SEA IAD Washington DC null
3080800.0 273.0 SEA IAD Washington DC null
3162225.0 174.0 SEA IAD Washington DC null
3201316.0 111.0 SEA IAD Washington DC null
3261311.0 104.0 SEA IAD Washington DC null
1111300.0 133.0 SEA PSP Palm Springs CA
1110910.0 171.0 SEA PSP Palm Springs CA
3170915.0 114.0 SEA PSP Palm Springs CA
3310645.0 179.0 SEA PSP Palm Springs CA
1161050.0 132.0 SEA SBA Santa Barbara CA
2091050.0 310.0 SEA SBA Santa Barbara CA
3191045.0 109.0 SEA SBA Santa Barbara CA
3241045.0 140.0 SEA SBA Santa Barbara CA
2122225.0 228.0 SEA CLT Charlotte NC
2142225.0 104.0 SEA CLT Charlotte NC
2152225.0 113.0 SEA CLT Charlotte NC
3081110.0 110.0 SEA CLT Charlotte NC
1290940.0 316.0 SEA ABQ Albuquerque NM
1171153.0 119.0 SEA PDX Portland OR
1171439.0 112.0 SEA PDX Portland OR
2091041.0 309.0 SEA PDX Portland OR
2090845.0 133.0 SEA PDX Portland OR
3021455.0 226.0 SEA PDX Portland OR
3021914.0 165.0 SEA PDX Portland OR
3090926.0 112.0 SEA PDX Portland OR
3251041.0 274.0 SEA PDX Portland OR
3261728.0 109.0 SEA PDX Portland OR
3301728.0 108.0 SEA PDX Portland OR
1112205.0 101.0 SEA MIA Miami FL
1262205.0 130.0 SEA MIA Miami FL
2142215.0 229.0 SEA MIA Miami FL
3292220.0 117.0 SEA MIA Miami FL
1012140.0 136.0 SEA SMF Sacramento CA
1010715.0 164.0 SEA SMF Sacramento CA
1021930.0 109.0 SEA SMF Sacramento CA
1031630.0 113.0 SEA SMF Sacramento CA
1041440.0 137.0 SEA SMF Sacramento CA
1041710.0 102.0 SEA SMF Sacramento CA
2211915.0 103.0 SEA SMF Sacramento CA
3262140.0 113.0 SEA SMF Sacramento CA
3271855.0 113.0 SEA SMF Sacramento CA
3191020.0 139.0 SEA SMF Sacramento CA
1291410.0 136.0 SEA PHX Phoenix AZ
1040830.0 294.0 SEA PHX Phoenix AZ
1300830.0 371.0 SEA PHX Phoenix AZ
1031510.0 119.0 SEA PHX Phoenix AZ
1061510.0 180.0 SEA PHX Phoenix AZ
1290720.0 147.0 SEA PHX Phoenix AZ
2082020.0 130.0 SEA PHX Phoenix AZ
2281855.0 186.0 SEA PHX Phoenix AZ
2110520.0 463.0 SEA PHX Phoenix AZ
2111132.0 107.0 SEA PHX Phoenix AZ
2160830.0 110.0 SEA PHX Phoenix AZ
2241132.0 107.0 SEA PHX Phoenix AZ
2251615.0 103.0 SEA PHX Phoenix AZ
3041455.0 108.0 SEA PHX Phoenix AZ
3051745.0 169.0 SEA PHX Phoenix AZ
3091455.0 126.0 SEA PHX Phoenix AZ
3251132.0 123.0 SEA PHX Phoenix AZ
3221530.0 121.0 SEA PHX Phoenix AZ
1060830.0 116.0 SEA DFW Dallas TX
1180830.0 132.0 SEA DFW Dallas TX
1281350.0 115.0 SEA DFW Dallas TX
1291545.0 247.0 SEA DFW Dallas TX
2031545.0 230.0 SEA DFW Dallas TX
2040830.0 135.0 SEA DFW Dallas TX
2061115.0 110.0 SEA DFW Dallas TX
2061545.0 125.0 SEA DFW Dallas TX
2061350.0 126.0 SEA DFW Dallas TX
2080830.0 356.0 SEA DFW Dallas TX
2090830.0 128.0 SEA DFW Dallas TX
3012320.0 123.0 SEA DFW Dallas TX
3152320.0 143.0 SEA DFW Dallas TX
3151400.0 146.0 SEA DFW Dallas TX
3301400.0 277.0 SEA DFW Dallas TX
1171220.0 110.0 SEA SFO San Francisco CA
1291220.0 103.0 SEA SFO San Francisco CA
1031125.0 107.0 SEA SFO San Francisco CA
1120924.0 268.0 SEA SFO San Francisco CA
1161058.0 131.0 SEA SFO San Francisco CA
1171058.0 138.0 SEA SFO San Francisco CA
1010955.0 104.0 SEA SFO San Francisco CA
1021914.0 105.0 SEA SFO San Francisco CA
1041830.0 131.0 SEA SFO San Francisco CA
1051214.0 139.0 SEA SFO San Francisco CA
1061214.0 384.0 SEA SFO San Francisco CA
1111310.0 124.0 SEA SFO San Francisco CA
1241310.0 133.0 SEA SFO San Francisco CA
1281310.0 250.0 SEA SFO San Francisco CA
1051855.0 166.0 SEA SFO San Francisco CA
2060955.0 148.0 SEA SFO San Francisco CA
2072125.0 105.0 SEA SFO San Francisco CA
2071845.0 203.0 SEA SFO San Francisco CA
2071220.0 139.0 SEA SFO San Francisco CA
2071100.0 113.0 SEA SFO San Francisco CA
2071405.0 144.0 SEA SFO San Francisco CA
2080955.0 121.0 SEA SFO San Francisco CA
2091835.0 124.0 SEA SFO San Francisco CA
2091405.0 101.0 SEA SFO San Francisco CA
2101220.0 134.0 SEA SFO San Francisco CA
2100955.0 107.0 SEA SFO San Francisco CA
2101100.0 105.0 SEA SFO San Francisco CA
2101405.0 105.0 SEA SFO San Francisco CA
2130955.0 108.0 SEA SFO San Francisco CA
2131100.0 139.0 SEA SFO San Francisco CA
2141100.0 107.0 SEA SFO San Francisco CA
2281100.0 130.0 SEA SFO San Francisco CA
2231058.0 136.0 SEA SFO San Francisco CA
2021310.0 115.0 SEA SFO San Francisco CA
2091820.0 149.0 SEA SFO San Francisco CA
2181526.0 106.0 SEA SFO San Francisco CA
2271905.0 154.0 SEA SFO San Francisco CA
2021450.0 139.0 SEA SFO San Francisco CA
2060950.0 150.0 SEA SFO San Francisco CA
2061450.0 140.0 SEA SFO San Francisco CA
2061855.0 119.0 SEA SFO San Francisco CA
2071855.0 146.0 SEA SFO San Francisco CA
2081330.0 164.0 SEA SFO San Francisco CA
2091450.0 106.0 SEA SFO San Francisco CA
2091855.0 182.0 SEA SFO San Francisco CA
2261450.0 259.0 SEA SFO San Francisco CA
2261855.0 224.0 SEA SFO San Francisco CA
2270950.0 174.0 SEA SFO San Francisco CA
2271450.0 240.0 SEA SFO San Francisco CA
2280950.0 207.0 SEA SFO San Francisco CA
2281450.0 331.0 SEA SFO San Francisco CA
2281855.0 124.0 SEA SFO San Francisco CA
3142043.0 101.0 SEA SFO San Francisco CA
3180950.0 155.0 SEA SFO San Francisco CA
3260950.0 117.0 SEA SFO San Francisco CA
3281430.0 112.0 SEA SFO San Francisco CA
3291050.0 138.0 SEA SFO San Francisco CA
3062055.0 113.0 SEA SFO San Francisco CA
3091028.0 143.0 SEA SFO San Francisco CA
3112055.0 116.0 SEA SFO San Francisco CA
3261043.0 121.0 SEA SFO San Francisco CA
3311043.0 257.0 SEA SFO San Francisco CA
3171237.0 182.0 SEA SFO San Francisco CA
3251933.0 197.0 SEA SFO San Francisco CA
3011330.0 115.0 SEA SFO San Francisco CA
3311045.0 189.0 SEA SFO San Francisco CA
3311440.0 101.0 SEA SFO San Francisco CA
1031152.0 397.0 SEA ATL Atlanta GA
1050830.0 106.0 SEA ATL Atlanta GA
1051152.0 107.0 SEA ATL Atlanta GA
1121159.0 201.0 SEA ATL Atlanta GA
1250630.0 206.0 SEA ATL Atlanta GA
1301159.0 117.0 SEA ATL Atlanta GA
1301322.0 179.0 SEA ATL Atlanta GA
2021159.0 145.0 SEA ATL Atlanta GA
2171320.0 133.0 SEA ATL Atlanta GA
3171320.0 109.0 SEA ATL Atlanta GA
1092015.0 119.0 SEA FAT Fresno CA
2012015.0 189.0 SEA FAT Fresno CA
2091150.0 232.0 SEA FAT Fresno CA
1021425.0 298.0 SEA ORD Chicago IL
1030600.0 103.0 SEA ORD Chicago IL
1081205.0 135.0 SEA ORD Chicago IL
1161205.0 582.0 SEA ORD Chicago IL
1241205.0 174.0 SEA ORD Chicago IL
1300815.0 209.0 SEA ORD Chicago IL
1021235.0 113.0 SEA ORD Chicago IL
1020830.0 151.0 SEA ORD Chicago IL
1051235.0 240.0 SEA ORD Chicago IL
1050830.0 163.0 SEA ORD Chicago IL
1241235.0 171.0 SEA ORD Chicago IL
1301235.0 111.0 SEA ORD Chicago IL
1300830.0 141.0 SEA ORD Chicago IL
1012359.0 227.0 SEA ORD Chicago IL
1040859.0 302.0 SEA ORD Chicago IL
1241110.0 223.0 SEA ORD Chicago IL
1311411.0 142.0 SEA ORD Chicago IL
2051235.0 115.0 SEA ORD Chicago IL
2050830.0 128.0 SEA ORD Chicago IL
2171235.0 204.0 SEA ORD Chicago IL
2170830.0 220.0 SEA ORD Chicago IL
2031615.0 185.0 SEA ORD Chicago IL
2171415.0 164.0 SEA ORD Chicago IL
2261415.0 138.0 SEA ORD Chicago IL
3120820.0 179.0 SEA ORD Chicago IL
3121200.0 151.0 SEA ORD Chicago IL
3200600.0 140.0 SEA ORD Chicago IL
3051235.0 140.0 SEA ORD Chicago IL
3120830.0 204.0 SEA ORD Chicago IL
3132240.0 127.0 SEA ORD Chicago IL
3162240.0 150.0 SEA ORD Chicago IL
3181417.0 127.0 SEA ORD Chicago IL
1091350.0 133.0 SEA MDW Chicago IL
1261350.0 109.0 SEA MDW Chicago IL
3171420.0 111.0 SEA MDW Chicago IL
3310600.0 206.0 SEA MDW Chicago IL
2271820.0 203.0 SEA COS Colorado Springs CO
3171825.0 205.0 SEA COS Colorado Springs CO
1250755.0 233.0 SEA JNU Juneau AK
1310755.0 210.0 SEA JNU Juneau AK
1311120.0 105.0 SEA JNU Juneau AK
3030755.0 110.0 SEA JNU Juneau AK
3130750.0 320.0 SEA JNU Juneau AK
1062320.0 107.0 SEA DTW Detroit MI
3121405.0 135.0 SEA ONT Ontario CA
3130725.0 174.0 SEA ONT Ontario CA
1171425.0 105.0 SEA LAX Los Angeles CA
1041700.0 264.0 SEA LAX Los Angeles CA
1051700.0 136.0 SEA LAX Los Angeles CA
1071645.0 151.0 SEA LAX Los Angeles CA
1311645.0 136.0 SEA LAX Los Angeles CA
1251020.0 130.0 SEA LAX Los Angeles CA
1261020.0 108.0 SEA LAX Los Angeles CA
1291258.0 126.0 SEA LAX Los Angeles CA
2022140.0 131.0 SEA LAX Los Angeles CA
2130610.0 135.0 SEA LAX Los Angeles CA
2091645.0 104.0 SEA LAX Los Angeles CA
2131645.0 134.0 SEA LAX Los Angeles CA
2031805.0 212.0 SEA LAX Los Angeles CA
2071805.0 105.0 SEA LAX Los Angeles CA
2071649.0 126.0 SEA LAX Los Angeles CA
2081649.0 154.0 SEA LAX Los Angeles CA
2091649.0 245.0 SEA LAX Los Angeles CA
2131705.0 107.0 SEA LAX Los Angeles CA
2161010.0 124.0 SEA LAX Los Angeles CA
2271149.0 192.0 SEA LAX Los Angeles CA
3141650.0 197.0 SEA LAX Los Angeles CA
3152105.0 115.0 SEA LAX Los Angeles CA
3171700.0 131.0 SEA LAX Los Angeles CA
3291700.0 118.0 SEA LAX Los Angeles CA
1050037.0 102.0 SEA MSP Minneapolis MN
1070700.0 193.0 SEA MSP Minneapolis MN
1130700.0 429.0 SEA MSP Minneapolis MN
2240655.0 109.0 SEA MSP Minneapolis MN
2121515.0 118.0 SEA MSP Minneapolis MN
1060800.0 132.0 SEA MCO Orlando FL
2220955.0 157.0 SEA SAN San Diego CA
3010955.0 108.0 SEA SAN San Diego CA
1031300.0 108.0 SEA ANC Anchorage AK
1062110.0 149.0 SEA ANC Anchorage AK
1132112.0 106.0 SEA ANC Anchorage AK
2072350.0 141.0 SEA ANC Anchorage AK
2091815.0 133.0 SEA ANC Anchorage AK
3181605.0 187.0 SEA ANC Anchorage AK
3231915.0 115.0 SEA ANC Anchorage AK
3311605.0 135.0 SEA ANC Anchorage AK
1022258.0 180.0 SEA JFK New York NY
1042258.0 285.0 SEA JFK New York NY
1022259.0 116.0 SEA JFK New York NY
2090715.0 110.0 SEA JFK New York NY
2022145.0 101.0 SEA JFK New York NY
2032145.0 165.0 SEA JFK New York NY
2031535.0 181.0 SEA JFK New York NY
2042145.0 201.0 SEA JFK New York NY
2142140.0 113.0 SEA JFK New York NY
2222140.0 118.0 SEA JFK New York NY
2032258.0 130.0 SEA JFK New York NY
2220700.0 404.0 SEA JFK New York NY
3310715.0 385.0 SEA JFK New York NY
3192140.0 119.0 SEA JFK New York NY
3091300.0 125.0 SEA JFK New York NY
1241000.0 806.0 SEA OGG Kahului, Maui HI
1030845.0 342.0 SEA PHL Philadelphia PA
1050845.0 174.0 SEA PHL Philadelphia PA
1210845.0 866.0 SEA PHL Philadelphia PA
1022215.0 121.0 SEA PHL Philadelphia PA
1031130.0 146.0 SEA PHL Philadelphia PA
1090835.0 148.0 SEA PHL Philadelphia PA
1170835.0 203.0 SEA PHL Philadelphia PA
2030845.0 202.0 SEA PHL Philadelphia PA
3130835.0 290.0 SEA PHL Philadelphia PA
1031810.0 142.0 SEA SLC Salt Lake City UT
1041016.0 117.0 SEA SLC Salt Lake City UT
1291725.0 111.0 SEA SLC Salt Lake City UT
1021555.0 175.0 SEA SLC Salt Lake City UT
1041825.0 110.0 SEA SLC Salt Lake City UT
2131635.0 134.0 SEA SLC Salt Lake City UT
2230710.0 739.0 SEA SLC Salt Lake City UT
2240710.0 477.0 SEA SLC Salt Lake City UT
2061005.0 119.0 SEA SLC Salt Lake City UT
3051315.0 123.0 SEA SLC Salt Lake City UT
3260710.0 149.0 SEA SLC Salt Lake City UT
3281750.0 125.0 SEA SLC Salt Lake City UT

Vertex Degrees

  • inDegrees: Incoming connections to the airport
  • outDegrees: Outgoing connections from the airport
  • degrees: Total connections to and from the airport

Reviewing the various properties of the property graph to understand the incoming and outgoing connections between airports.

// Degrees
// The number of degrees - the number of incoming and outgoing connections - for various airports within this sample dataset
display(tripGraph.degrees.sort($"degree".desc).limit(20))
id degree
ATL 179774.0
DFW 133966.0
ORD 125405.0
LAX 106853.0
DEN 103699.0
IAH 85685.0
PHX 79672.0
SFO 77635.0
LAS 66101.0
CLT 56103.0
EWR 54407.0
MCO 54300.0
LGA 50927.0
SLC 50780.0
BOS 49936.0
DTW 46705.0
MSP 46235.0
SEA 45816.0
JFK 43661.0
BWI 42526.0

City / Flight Relationships through Motif Finding

To more easily understand the complex relationship of city airports and their flights with each other, we can use motifs to find patterns of airports (i.e. vertices) connected by flights (i.e. edges). The result is a DataFrame in which the column names are given by the motif keys.

/*
Using tripGraphPrime to more easily display 
- The associated edge (ab, bc) relationships 
- With the different the city / airports (a, b, c) where SFO is the connecting city (b)
- Ensuring that flight ab (i.e. the flight to SFO) occured before flight bc (i.e. flight leaving SFO)
- Note, TripID was generated based on time in the format of MMDDHHMM converted to int
- Therefore bc.tripid < ab.tripid + 10000 means the second flight (bc) occured within approx a day of the first flight (ab)
Note: In reality, we would need to be more careful to link trips ab and bc.
*/
val motifs = tripGraphPrime.
  find("(a)-[ab]->(b); (b)-[bc]->(c)").
  filter("(b.id = 'SFO') and (ab.delay > 500 or bc.delay > 500) and bc.tripid > ab.tripid and bc.tripid < ab.tripid + 10000")

display(motifs)

Determining Airport Ranking using PageRank

There are a large number of flights and connections through these various airports included in this Departure Delay Dataset. Using the pageRank algorithm, Spark iteratively traverses the graph and determines a rough estimate of how important the airport is.

// Determining Airport ranking of importance using `pageRank`
val ranks = tripGraph.pageRank.resetProbability(0.15).maxIter(5).run()
ranks: org.graphframes.GraphFrame = GraphFrame(v:[id: string, City: string ... 3 more fields], e:[src: string, dst: string ... 5 more fields])
display(ranks.vertices.orderBy($"pagerank".desc).limit(20))
id City State Country pagerank
ATL Atlanta GA USA 18.910104616729814
DFW Dallas TX USA 13.699227467378964
ORD Chicago IL USA 13.163049993795985
DEN Denver CO USA 9.723388283811563
LAX Los Angeles CA USA 8.703656827807166
IAH Houston TX USA 7.991324463091128
SFO San Francisco CA USA 6.903242998287933
PHX Phoenix AZ USA 6.505886984498643
SLC Salt Lake City UT USA 5.799587684561128
LAS Las Vegas NV USA 5.25359244560915
SEA Seattle WA USA 4.626877547905697
EWR Newark NJ USA 4.401221169028188
MCO Orlando FL USA 4.389045874474043
CLT Charlotte NC USA 4.378459524081744
DTW Detroit MI USA 4.223377976049847
MSP Minneapolis MN USA 4.1490048912541795
LGA New York NY USA 4.129454491295321
BOS Boston MA USA 3.812077076528526
BWI Baltimore MD USA 3.53116352570383
JFK New York NY USA 3.521942669296845

BTW, A lot more delicate air-traffic arithmetic is possible for a full month of airplane co-trajectories over the radar range of Atlanta, Georgia, one of the busiest airports in the world.

See for instance:

Using the tripGraph, we can quickly determine what are the most popular single city hop flights

// Determine the most popular flights (single city hops)
import org.apache.spark.sql.functions._

val topTrips = tripGraph.edges.
  groupBy("src", "dst").
  agg(count("delay").as("trips"))
import org.apache.spark.sql.functions._
topTrips: org.apache.spark.sql.DataFrame = [src: string, dst: string ... 1 more field]
// Show the top 20 most popular flights (single city hops)
display(topTrips.orderBy($"trips".desc).limit(20))
src dst trips
SFO LAX 3232.0
LAX SFO 3198.0
LAS LAX 3016.0
LAX LAS 2964.0
JFK LAX 2720.0
LAX JFK 2719.0
ATL LGA 2501.0
LGA ATL 2500.0
LAX PHX 2394.0
PHX LAX 2387.0
HNL OGG 2380.0
OGG HNL 2379.0
LAX SAN 2215.0
SAN LAX 2214.0
SJC LAX 2208.0
LAX SJC 2201.0
ATL MCO 2136.0
MCO ATL 2090.0
JFK SFO 2084.0
SFO JFK 2084.0

Top Transfer Cities

Many airports are used as transfer points instead of the final Destination. An easy way to calculate this is by calculating the ratio of inDegree (the number of flights to the airport) / outDegree (the number of flights leaving the airport). Values close to 1 may indicate many transfers, whereas values < 1 indicate many outgoing flights and > 1 indicate many incoming flights. Note, this is a simple calculation that does not take into account of timing or scheduling of flights, just the overall aggregate number within the dataset.

// Calculate the inDeg (flights into the airport) and outDeg (flights leaving the airport)
val inDeg = tripGraph.inDegrees
val outDeg = tripGraph.outDegrees

// Calculate the degreeRatio (inDeg/outDeg), perform inner join on "id" column
val degreeRatio = inDeg.join(outDeg, inDeg("id") === outDeg("id")).
  drop(outDeg("id")).
  selectExpr("id", "double(inDegree)/double(outDegree) as degreeRatio").
  cache()

// Join back to the `airports` DataFrame (instead of registering temp table as above)
val nonTransferAirports = degreeRatio.as("d").join(airports.as("a"), $"d.id" === $"a.IATA").
  selectExpr("id", "city", "degreeRatio").
  filter("degreeRatio < 0.9 or degreeRatio > 1.1")

// List out the city airports which have abnormal degree ratios
display(nonTransferAirports)
id city degreeRatio
GFK Grand Forks 1.3333333333333333
FAI Fairbanks 1.1232686980609419
OME Nome 0.5084745762711864
BRW Barrow 0.28651685393258425
// Join back to the `airports` DataFrame (instead of registering temp table as above)
val transferAirports = degreeRatio.as("d").join(airports.as("a"), $"d.id" === $"a.IATA"). //degreeRatio.join(airports, degreeRatio("id") === airports("IATA")).
  selectExpr("id", "city", "degreeRatio").
  filter("degreeRatio between 0.9 and 1.1")
  
// List out the top 10 transfer city airports
display(transferAirports.orderBy("degreeRatio").limit(10))
id city degreeRatio
MSP Minneapolis 0.9375183338222353
DEN Denver 0.958025717037065
DFW Dallas 0.964339653074092
ORD Chicago 0.9671063983310065
SLC Salt Lake City 0.9827417906368358
IAH Houston 0.9846895050147083
PHX Phoenix 0.9891643572266746
OGG Kahului, Maui 0.9898718478710211
HNL Honolulu, Oahu 0.990535889872173
SFO San Francisco 0.9909473252295224

Breadth-first search (BFS) is designed to traverse the graph to quickly find the desired vertices (i.e. airports) and edges (i.e flights). Let's try to find the shortest number of connections between cities based on the dataset. Note, these examples do not take into account of time or distance, just hops between cities.

// Example 1: Direct Seattle to San Francisco
// This method returns a DataFrame of valid shortest paths from vertices matching "fromExpr" to vertices matching "toExpr"
val filteredPaths = tripGraph.bfs.fromExpr((col("id") === "SEA")).toExpr(col("id") === "SFO").maxPathLength(1).run()
display(filteredPaths)

As you can see, there are a number of direct flights between Seattle and San Francisco.

// Example 2: Direct San Francisco and Buffalo
// You can also specify expression as a String, instead of Column
val filteredPaths = tripGraph.bfs.fromExpr("id = 'SFO'").toExpr("id = 'BUF'").maxPathLength(1).run()
filteredPaths: org.apache.spark.sql.DataFrame = [id: string, City: string ... 2 more fields]
filteredPaths.show()
+---+----+-----+-------+
| id|City|State|Country|
+---+----+-----+-------+
+---+----+-----+-------+
display(filteredPaths) // display instead of show - same diference

But there are no direct flights between San Francisco and Buffalo.

// Example 2a: Flying from San Francisco to Buffalo
val filteredPaths = tripGraph.bfs.fromExpr("id = 'SFO'").toExpr("id = 'BUF'").maxPathLength(2).run()
display(filteredPaths)

But there are flights from San Francisco to Buffalo with Minneapolis as the transfer point.

Loading the D3 Visualization

Using the airports D3 visualization to visualize airports and flight paths

Warning: classes defined within packages cannot be redefined without a cluster restart.
Compilation successful.
d3a1.graphs.help()

Produces a force-directed graph given a collection of edges of the following form:
case class Edge(src: String, dest: String, count: Long)

Usage:
%scala
import d3._
graphs.force(
  height = 500,
  width = 500,
  clicks: Dataset[Edge])

// On-time and Early Arrivals
import d3a1._

graphs.force(
  height = 800,
  width = 1200,
  clicks = sql("select src, dst as dest, count(1) as count from departureDelays_geo where delay <= 0 group by src, dst").as[Edge])